Any tips/tricks to not feel odd just getting up and stretching? What specific stretches can I do in the time frame that are also good for public use if necessary?

I stretch when I wake up and just after dinner, so it feels pretty natural to stretch when I'm yawning or at the end of the day. For public stretches, you could go for the cross body shoulder stretch, overhead shoulder stretch, rolling your shoulders and your neck. All good to do at the desk ☺️

Any standing stretches will work and also if you are sitting you can do stretches by sitting and also if you are laying down then you can do any laying down stretches.

I personally do contortion so I am used to stretching myself and do it quite a lot so I feel i am not the right person to tell you how to get up and stretch but it makes it easier if you have a yoga mat right at the bottom of your bed or even do your stretches in your bed.

Mainly neck and shoulder stretching. They can be done while standing or sitting and they don't require much movement but the are so refreshing and relieving