DK1 - thanks for the suggestion! We'll keep that in mind as we consider future template scenarios.
Mohammad Khatibi P_ITGeek_CA mattchowell - site templates is now rolled out to 100% worldwide, so all site owners should be able to access the template gallery and apply a template to their site from Settings > Apply a site template. In Mohammad's screenshot, the tip in the Next steps panel is an additional entry point to open the template gallery. The pop-up dialog featured in the GIF is currently rolling out, so you should see it soon in the next couple weeks.
Arknev rumispoint1 - I've seen some reports from customers that experienced something similar - they needed to update the web template ID for a previously uploaded site template using Set-SPOSiteDesign. Use value "64" for a team site template, value "68" for a communication site template, and value "1" for a non-group team site template (or if you've restricted/disabled modern M365 group creation). Looks like you were able to resolve your issue by re-adding, though.
kparkkinen - That is correct that the dropdown has been removed with the release of site templates. Thank you for taking the time to share such thorough feedback, and I hear your pain points here. We do have improvements planned for the site creation experience, so will take this feedback into consideration as we continue to update it.
alongoldberg - Following up on my earlier response to you, we are currently working on admin controls so you can manage hiding/displaying Microsoft-provided templates. This has been added to the roadmap under Feature ID #85566. We are planning to roll that out soon (hopefully early CY2021Q4), but please stay tuned to Message Center post announcements for the most accurate timeline.