Which is where we come to execution. Finding activities and timing that generates connection is hard. For example, whatever your company is picking absolutely does not engender in you what they are hoping to engender.
The downside of being unhappy during 'irrelevant' activities or not joining them is that work is by and large a communal activity. The water cooler is still a good metaphor even when your work does not have any other them around.
Are there activities you and others enjoy that you could suggest? Even if just for your team and closest stakeholders.
Also: as someone else pointed out, mandatory should equate "during work time for which I am paid." The rest is optional.