In answer to a question and keeping this in layman's terms:
Key concept - all generating plant in an AC power system ("grid") is in parallel and so is all load.
In other words, each generating unit is generating into a single AC power system. Everything from the 750MW, that's 750,000,000 Watts, steam driven unit at Kogan Creek (Qld) which is the largest single generating unit in Australia down to someone's little 1.1kW (1100 Watts) Sunny Boy solar system installed 15 years ago in the early days of rooftop solar are all in parallel, they're all ultimately supplying into that same AC power system. There's a lot of circuit breakers, distribution and transmission lines, transformers and so on between them yes but it's a single system as such.
Likewise all load is drawing from that same system. Everything from your table lamp to an aluminium smelter, they're all just loads in parallel albeit some much larger than others and some supplied directly from the transmission system (smelters etc) and the rest supplied via the distribution network.
System frequency in Australia is nominally 50Hz and so long as total generation matches total load, including losses, it'll remain stable.
More generation than load and frequency will rise.
Less generation than load and frequency will fall.
Same concept as a car speeding up or slowing down if the mechanical power from the engine doesn't match the load placed upon it. That there's some lag, that frequency will rise or fall gradually rather than abruptly changing to a new value, largely coming down to physical inertia. The many tonnes of rotating machinery does take some energy to speed up or slow down (and that's a good thing not a bad thing).
For the main grid in Australia, the NEM (National Electricity Market) mainland power system (covering most of Qld and effectively all of NSW, ACT, Vic and SA apart from isolated remote towns etc) the frequency standard is:
Nominal = 50.00 Hz
Under normal operating conditions in the range 49.75 - 50.25Hz, with at least 99% of the time in the range 49.85 - 50.15Hz.
Under fault conditions, the sudden unexpected failure of generation, transmission or disconnection of major load, the most extreme acceptable limits are 47.00 to 52.00 Hz. Noting those are extreme values that would never be done intentionally and ideally should never occur.
Tasmania has a variation in that the upper extreme limit in the event of major faults is 55.00 Hz. Otherwise it's the same standard as the mainland NEM states including the aim to contain frequency to 52Hz under any "normal" fault scenario. Noting that the physical connection between the mainland and Tasmania is DC such that whilst energy transfer can and does occur routinely, the mainland and Tasmanian systems aren't synchronised as such, frequency can vary between the two.
Places not part of the NEM have different standards, due to technical factors, but they're not much different in practice, they all aim to keep system frequency within a few % of 50.00 Hz under all circumstances.
The reason for such precision being once it's outside that range the chance that it ends badly becomes rapidly greater, especially for under frequency, because generating units will themselves trip due to low frequency and it doesn't need much below the lower bound, 47Hz, to see that happen. So a lack of generation causes a further lack of generation and from there it's an extremely rapid slide into the abyss.
In theory Under Frequency Load Shedding (UFLS), which is the automatic disconnection of loads in a pre-determined order, should arrest any major fall in frequency. However it does so by the brutal method of leaving consumers without power so is never a preferred occurrence and could be likened to the air bag deploying in a car. Beats being killed but definitely not good as such, it's a last line of defence and, crucially, there's no guarantee it'll be sufficient - plenty of incidents around the world where it wasn't.
In the Australian context under normal circumstances the preferred means of maintaining system frequency is ultimately market driven. FCAS (Frequency Control Ancillary Services) is the official term and in short that's market driven in that any generating plant with the technical capability can offer a price for the service, and it's the cheapest that'll be picked subject to satisfying technical requirements. There's no bias toward any particular technology there - it's simply technical ability and whatever price the owner (well, the traders they employ) offer.
That results in there being no generating plant specifically dedicated to that function. Yes in practice some will tend to offer the best price, and that'll be influenced by technology (the big batteries have a definite advantage there), but under varying conditions which facilities are being used for that purpose will vary. Noting that due to the scale of requirements multiple units will be used in practice.
For the third quarter of 2023, batteries provided 40% of FCAS, coal 25%, hydro 15%, 13% demand response (heavy industry mostly) and the remaining 6% was split between gas, diesel, wind, solar. Figures don't add to 100% due to rounding.
Contrary to popular belief, wind and solar can do it under the right circumstances. Eg they can't offer an increase in output if they're already fully utilising the wind or sun, but they certainly can offer a decrease in output as a contingency measure. etc. Likewise a battery that's fully charged can't do the decrease but it can do the increase. Put them together and it works and AEMO's system can easily cope with sending different instructions to different units.
If all that fails though, well there's always primary frequency control at the machine level which is just the generating unit itself responding to frequency deviations without any external direction to do so. In very simple terms that's speed governors on generating plant, albeit rather complex ones, and it's the natural response of loads to any deviation in frequency. That's raw engineering stuff - it's at odds with the modern era thinking that says someone ought offer a price and be paid to do it, it's just the machine doing it itself.
Which brings up the point that the idea of having a market for FCAS is a completely human construct, it's not something fundamental to power systems. Go back 30 years and there was no such concept, it's just something that was an inherent feature of generating plant and running a power system. That it's viewed differently today being a political and economic construct not an engineering one - it stems from having multiple owners of generation in the same power system and the ideological view that they ought be competing against each other on price not only for energy but for FCAS as well.
There was quite a battle over that one, engineers versus politics and economics, and it's a case where the engineers did ultimately succeed in making the point that primary frequency control is a necessity. If there's also some other system then OK, we can live with that even though it seems overly complex (a market for the sake of a market), but primary control must always be there - that it doesn't fit with the market idea doesn't change that need, political or economic ideas don't overcome physics. Suffice to say there was quite a battle over that one, mostly out of public view.
So in short, there's no single answer. There's no generating unit specifically tasked with maintaining a stable frequency but rather, there's a procurement of FCAS for every dispatch interval and who does it comes down to the price offered. Politics and economics prefers that approach whilst engineers aren't keen, generally seeing it a an unnecessarily complex process.