The King's Avatar - This is a friendship/(e)sports drama. There's no romance.
Six Flying Dragons - You have this On Hold, but I recommend this drama very highly. Both of the main characters are male. There is a bit of romance, but the politics is the real focus of the show. And after a while the romance turns more into a partnership.
Faith - Though the romance definitely has a major focus (there's a lot of politics too), I'm adding this because I feel like the romance fits the description "connection but less skinship." I don't actually remember it that well, but I remember thinking that the main couple sometimes felt more like companions than lovers.
Bad Guys - I don't think there's any romance. Most of the main characters are all male. It's a crime show.
Boku no Ita Jikan - This is definitely a romance, but it's definitely not a fluffy rom com type. It's about dealing with an incurable disease. 1 Litre no Namida has a similar subject matter and I believe it has less romance. I haven't watched it, but it's supposed to be really good.
My Mister - I haven't completed this show yet. I'm actually not sure whether the relationship between the leads will end up romantic or not, but it's certainly a mature story (in terms of theme, not explicit content). So far it's really good!
My Country - I don't remember the romance. I think there is one, but it's more focused on the bromance and politics.
Nobuta wo Produce - This is a show about friendship.
14-sai No Haha - There's kinda a romance, but it's really about teen pregnancy.
Arthdal Chronicles - So far (still waiting for season 2), there are hints of romance, but it's really a politically focused show.
White Christmas - I don't remember this having any romance. It's a phycological thriller.
IRIS - There's definitely a romance (and there might seem like a lot in the first couple episodes), but the majority of the show is an action/espionage story. The male and female leads are actually separated though most of it.
Vagabond - I'm not sure if there's romance, if there is, there's not much. It's also an action/espionage show.
Man to Man - This has more romance than IRIS or Vagabond, especially in the second half, but it also is very focused on the action/espionage plot.
Reply 1988 - This does have quite a bit of romance, but I would really say it's more a show about family and friendship.
Lawless Lawyer - There's definitely a romance, but it's a legal/crime drama. I don't remember too much focus on the romance.
You're All Surrounded - Another crime drama with minimal romance.
Two Weeks - I never finished it, but there was no romance up to episode 11. It's more action/thriller.
Bloody Monday - I haven't finished it, but I don't think it's romance focused (I don't remember any so far). Again an action/thriller/espionage type show.
Misaeng - I don't remember much romance. It's a workplace drama.
Prison Playbook and SKY Castle are highly regarded shows that I don't think are romance focused, though I haven't seen them. I'm sure there are a lot more ...
