Are there block explorers for Bitcoin that would let me check the balance for a given date/height? Or any other option/tool like an API?
E.g. OXT.me shows the level of funds corresponding to an address over time.
I'm not aware of any site that shows this information more precisely. However, many block explorers allow you to export the sequence of transactions that interacted with an address. You can use the corresponding transactions to create a sequence of the amounts added and deducted from the address at specific block heights and dates. With such a list you could easily calculate the funds for every date or block height.