Maybe even signet can be adapted for this so that a new chain doesn't have to be created, but I don't know if that is possible or if it would require a new chain entirely.
You can always claim less coins in the coinbase transaction, than you are allowed to. It is a perfect no-fork, not even a soft-fork. If you can claim 0.01220703 tBTC today, then it is the upper amount. You can as well always claim zero coins in the coinbase transaction, and your blocks will be perfectly valid in all networks: mainnet, signet, regtest, and testnet3.
That being said, the Bitcoin Core team is not too thrilled about the prospect of modifying the current chains.
Yes, but the situation is not so simple. If developers could simply pull off the plug, and destroy testnet3, by detaching it from the current client, then they would probably do so. But instead, they ask, if there should be any "grace period" or something, because they know, that people can simply stay with the old software. And in that case, testnet3 may become just another altcoin, probably much closer to the mainnet than many other altcoins.
And also, there is some risk of replaying coinbase transactions between networks. Which means, that if you have some block 1,234,567 in the current testnet3, then you can migrate exactly the same coinbase transaction into testnet4. And similar things can happen between signet and testnet4, or even mainnet and testnet4. One of the things, preventing that from happening, is the fact that testnet3 has much more blocks than other networks. Which means, that blocks from testnet3 can be copy-pasted into other networks, but not the other way around, because it would require a huge chain reorganization in testnet3.