Is it possible to run a pruned node while being able to verify any TXID?
You're asking two different things, so it's not clear which answer is correct.

Yes, a pruned full node verifies all transactions. That's why it's still called a full node.

No, pruning is not compatible with txindex.

But, are you sure you need txindex? If you're only receiving payments to yourself you don't need txindex.