Considering the holidays are supposed to be times filled with cheer, the stress levels that people feel is incredible. There is less time, there is more to do, and, with the pandemic, things may be totally different for people this year. My family visits are usually fairly easy to plan, but who knows what will happen this year?
The best thing you can do as a manager is acknowledge it and discuss with individuals and as a team how you can help. If you've built a good relationship with your team, they will be honest.
Some things to consider:
Projects: You most likely can't take projects off their plate, but you might be able to speed things along or work with them to overcome some obstacles.
Holiday parties: the holidays bring extra responsibilities to a lot of people. Gatherings, school events, etc. It might be better to do something after the holidays when things have slowed down for some people. In some cases, maybe you can do something during the workday (like a holiday lunch). Just be careful, someone who is swamped with a project may either not go or have to work late or weekends because of your nice lunch.
Gifts: First, set the expectation that no one on your team should buy you a gift. Beyond being inappropriate, it is just too dangerous. If you decide to buy your team gifts, try to make it personal. For me, when I read a professional book I really liked during the year, I would buy and extra copy. Then I would give them as gifts. I always stressed that this was not a hint on their performance, but something I thought they might like. As for gifts between employees, that is something the team should decide. However, keep in mind that this has been a tough year and financially it might be a strain on some people (who might be too embarrassed to say anything). I knew one manager who held a Secret Santa, but told anyone who did not think they could afford it to tell them in private. If someone said something, he had a stack of gift cards they could use to buy the gift. No one besides that person ever knew.
Personal difficulties: Holidays can be hard because of the loss of a loved one or just bad family memories. Obviously, you can't be a therapist, but you can be sensitive to these feelings. Empathize and ask what you can do to help.
This isn't an exhaustive list, but it should be enough to get you started.