Displaying multiple tags in user list item together with other components

I have a page where I need to display users in a list, like this:

In every item I will need to display many tags, there can be one or two, or much more, like ten and even more. The current look and placement can be adjusted, it can go on two lines also.

What would be a good solution from UX perspective and also how to show them visually?

I made two versions. The 1st one is a solution to display first three + tag that indicates how much in total they are, so that user clicks un them, for example, it will show modal with all tags.

The 2nd version is visually not so appealing, but can show them all.

This also should work on smaller screens. Maybe someone worked on something similar and can give some valuable advice. Thanks!