There is no real standard for mesh systems they are all proprietary. Even the simple repeater function is not actually part of the wifi standards.
Even within the same vendor their different lines of routers/mesh systems may not work together. It is a huge mess......best if you can find a different solution than any kind of mesh.
You would have to read all the fine print on the devices. Most the ones I have seen that let a repeater run a second repeater off it have extra dedicated radio chips for the backhual. This makes the units much more expensive since you now have 3 or maybe even 4 radio chips.
Part of the reason the units talk to the main router is every hop you put in the path will cut your speed by half. So a path with 2 repeaters in it you will only get 25% of the maximum rate and likely much less since you now have 3 signals rather than just 1 than can be interfered with.
The best solution tends to be to not use wifi to connect between the main router and the remote radios. Best if you can run a ethernet cable. If that is not a option and you have coax wire in both rooms you can use MoCA. If neither of those is a option you can try powerline, make sure you get the newer 1000 or 2000 number units. All these appear as a ethenet cable between the main router and remote radio which is running as a AP and not a repeater. This is how corporations run wifi they do not use mesh/repeaters.
This type of solution will massively outperform most mesh repeater systems.