Wallet and Pay and Reminders disappeared after re-pairing Apple Watch with watchOS 6.1
Accidentally, I found the solution, which I'd like to share here:

Reminder app has never appeared in the list of installed apps, neither in the Watch app on the iPhone, nor on the Apple Watch itself (in contrast to Calendar, and in contrast to the situation before the upgrade to watchOS 6).

BUT: while configuring the watch facet, I saw Reminder as a possible complication to choose. I tried it to select and it opened the new version of Reminders app. It was a bit laggy, but it worked: all reminders were synchronized with the iPhone.