Let's assume the Taproot soft fork is activated in June 2021. I continue to run an old version of Bitcoin Core (not enforcing Taproot rules) in July 2021 and so my full node treats valid Taproot spends as anyone-can-spend. Then in August 2021 I upgrade to the latest version of Bitcoin Core and start enforcing the Taproot rules. Does my full node re-verify the Taproot spends from the point of activation or does it only verify Taproot spends from the point that I upgraded to the latest version of Bitcoin Core?
I'm pretty sure that your node will never re-verify those transactions according to the Taproot rules unless it is forced to do a new initial block download (IBD) due to database corruption etc. It verified them at the time as valid spends according to anyone-can-spend rules and so there is no need to revisit them. (I will correct at a later date if this is false).
There is some interesting advice and observations on bitcoincore.org in the Segregated Witness Upgrade Guide. Some of it is specific to the SegWit soft fork (e.g. activation) rather than the proposed Taproot soft fork but much of it is applicable to both.