How to welcome new PhD students/postdocs to the group during lockdown?
Here are some things the grad students in my department did to keep connected:

We have a slack group with lots of channels. Some are dedicated to posting memes/talking about random things

We have occasional game nights on Zoom where we play games like Contact and other games that can be played over Zoom.

We sent emails specifically to the new grad students (even though there were only two of them) to check up on them, invite them to our slack group etc. One of the two did start participating quite frequently in our Slack conversations so that was successful.

Also, depending on how careful you need to be with Covid, I think you really can get coffee together. If you're a grad student, and you are new to the city, it's going to be really really lonely staying in your apartment possibly alone and never meeting anyone. Getting coffee or takeout and hanging out outside while socially distanced with one or two people every once in a while is probably a relatively low-risk activity and unless you're particularly vulnerable, I would say it's probably healthier than having no contact with anyone whatsoever.

Along those lines you can also ride bikes, play tennis, or go running together. These things are pretty low-risk depending on where you live. Where I live, there are public outdoor tennis courts that are not very crowded so you don't need to be close to anyone. Exercise has helped me cope with isolation a lot and really improves my productivity.