About 5 weeks ago, I decided to accept a TT assistant professor position at a R1 University in US, and was told to wait for 1-2 weeks for an official (electronic) letter arriving since it would go through the internal HR processes before being ready for signing. At this moment, I have not received further updates about the letter. I think the process may take more time than expected because of the Covid-19. But is it appropriate to send out a follow-up email? Or just watch for their notice? If the letter has no harm, any suggestions to draft one? Many thanks in advance.
You can probably safely wait a bit longer for the reasons you suggest. The staff that normally handles such things may not have complete access to their office systems and may be poorly supported for distance work.
There is some turmoil generally in hiring now and if the university is part of a State system they will be bound by directives from the legislature. But there is nothing you can do to affect that in any case.
So don't wait more than another week and ask for an update. Just note that you don't have the official notice yet and would like an update.
If you have other offers pending with deadlines don't wait too close to those deadlines to ask for the update. I don't expect bad things to happen, but it is hard to make predictions in times of chaos.