First, get off the AI.  It is wasting everyone's time here and may well be driving you astray.  Although it can be handy when you don't even know the terms to search, once you're actually talking to people on a subject the AI provides no or negative value because they frequently hallucinate and always sound authoritative when they do it.  Chatbot  style AI is even known to produce psychosis like symptoms in some people.  Plus because fraudsters are now frequently using AI you're just making yourself sound like one. Respond with another AI generated message and I will nuke your account for wasting everyone's time with AI-spam.

If a transaction is included in a block you can save the inclusion proof.  Bitcoin Core's wallet has all the commands to do it, it just doesn't do it automatically anymore. It used to save them for your own transactions, but it bloated up wallets and absolute no one was using it-- and you can always extract them yourself from any archive node that witnessed them, since other than pruning blocks are never deleted even if the block is now stale.    The inclusion proofs are extracted with the gettxoutproof command and can be verified by the verifytxoutproof.  This still works even for stale blocks.

I dunno about other wallet software, as everything but bitcoin core is trash, but in Bitcoin Core all of the user's own transactions in it are maintained by the wallet-- even if the blocks confirming them are made stale or even if the transaction is orphaned (meaning the parent block that generated the coins it is spending is eliminated, which would require a 100 block+ reorg for any non-generation transaction).   There is no need for txindex, as you can just see your transactions in the wallet.   If they were ever confirmed you can extract a txoutproof that anyone else can verify.

The blockchain itself is already the log you seek, your own wallet is already the log you seek.  Any kind of public log is going to have limitations arising from an admissions policy, otherwise spammers can just overload it.  Your own wallet doesn't have that issue, however.   Plus although they provide no automatic access all archive nodes remember all stale blocks and could extract proofs, if you foolishly didn't use a good wallet or didn't keep it around if you know the txid it could still be found.

On what basis do you believe that they did?  How do you know you haven't been lied to / tricked by someone or have not given yourself a false memory.   For years I have routinely received emails from people who have lost touch with reality and are absolutely convinced that they purchased bitcoin in 2004 or whatever other unambiguously impossible situation.  Some people fixate on a dream of bitcoin riches and then gradually forget that they're just dreams.

Mostly people have kept their wallets, which will include the transactions.

In any case, if you provide the address(es) and the height range when you say they were confirmed then perhaps someone here with a older node will scan their blockchain files for the transactions for you.  You can increase the odds of someone doing that by explaining in an convincing and non-AI way why you know they had previously confirmed payments to them.  Keep in mind that the bar on that is kinda high because very few confirmed transactions have ever been reorged out and not restored (which can happen due to doublespends, if they're just reorged out alone nodes will try to restore them until they are conflicted).