Every TapScript output uses SHA-256 internally, so if you keep using that, then it should be fine. If SHA-256 will ever be broken, then it can break everything, including Proof of Work, all ECDSA signatures, and also large parts of the Internet behind Bitcoin. Which means, that many things already rely on SHA-256, and you can do that too, because if the world will burn, then the security of your coins will be doomed anyway, if the attacker will be able to overwrite Proof of Work, which created your coins in the first place.

Of course, SHA-256 can be patched in a similar way, as SHA-1 was, by making a hardened version, which will protect it only from particular attack vectors.