Current repo implementation does not count viewing time towards timed Drop rewards.

The example I looked at needs to be claimed (button clicked) every hour to continue earning towards watched time. So simply going afk only ever builds up time for 1 drop. You can Claim via a popup message box in chat (same as channel points) or via the inventory page, you could have multiple claim buttons here. I've included code for both buttons should they require css descriptors.

twitchchatclaimbutton.txt
twitchinventoryclaimbutton.txt

I assume this also means other types of Drop reward are not able to be collected?

Solution could be to keep the channel stream open, which I don't believe currently happens, clicking the claim button when it appears. Most pages have the "drops enabled" tag so wouldn't need to happen if no drops enabled. Or a periodic check of your inventory for available items to be claimed could be a simpler catch-all (assuming watch progress starts to be recorded).