not recommended...
Maybe your competitors are doing it because they\re in for the short term and they don't care they'll get caught (how long have your competitors been the same for, and how long have they been having the linkwheel for? If you can figure this out you can guesstimate whether or not they give a crap)...
It's also possible that your competitors are actual businesses (with brick and mortar offices and stuff) but they have multiple sites, so they're mentioning all of their sites on each one of their sites somewhere in the footer. Weirdly enough, I've seen stuff like this never get penalized, maybe google considers them unaware of what they're doing and lets them get away with it, or maybe google has a rule amongst their billions of retarded rules against this type of practice for real companies, you never know which trick google pulls out of their sleeve next (like, for example, lately they've started blacklisting the entire internet just because they're pissed that humans dare to use their domains and sites for whichever they want. The nerve on people to do with their sites whatever they want, how dare they!)
Anyway, the point is that just because your competitors are doing it you shouldn't do it either. Linkwheels are one of the most surefire ways of getting penalized, especially if you're going to link all sites in your network together. If you have 4 sites, for example, and link from site 1 to sites 2,3, and 4 and stop there you might get away with it.
But if you go 1-2-3-4-1... well, this is the perfect example of a punishable linkwheel and your days are numbered (for ALL sites in your network)
And like HenryObi said, interlinking all sites in a network when they're all in the same GSC account is especially bad, and it's not only about GSC. If your sites use GA or other google products that google can link to the same IP or google account (yours) can get you into troubles...
Personally, I'd not do it, but if you're desperate.... your call I guess
