I'm wondering if this would not be a hard-forking change. Can you really achieve this only "tightening" some rules?
One crucial question is: How would old nodes process these transactions? If they see a transaction with several inputs, they may automatically deduce that all of them are spent. So I guess there would need to be a completely new input format, like Segwit did. But it would be a much more drastic change than Segwit imo.
Googling the concept I found
this - they claim to have "implemented ring signatures in Bitcoin". They however don't provide much details, only a JavaScript (!) file. So either I'm not knowledgeable enough to understand what they were doing, or it's not really a "ring signature implementation" on Bitcoin but perhaps a Proof of Concept (which could be implemented in an altcoin).
What should work however is to create a 1:1 pegged token (via Proof of burn) on the Bitcoin chain using OP_RETURN or another "data storage" format (Bitcoin Stamps, Ordinals Inscriptions ...) to code in the necessary data for ring signatures (OP_RETURN may be actually to limited currently). I think I wouldn't make many friends here if I'd implemented that
