Should I Initiate date 3?

I've gone on 2 dates with a guy 2 weeks in a row. For week 3 he was away on a trip. We saw each other the Wed before the trip but I haven't seen him in 11 days now. He reaches out quite frequently - I'd say even up to multiple times a day. It's a bit low effort though like a "hey, how's it going?" often not super personalized like a "good morning" text that for some reason my intuition is saying this guy might be a player and texting this to 5 other girls at the same time ... especially so early on it seemed like a lot, but he was planning dates so it didn't matter so much.

Couple more things: He said before leaving "guess I could have planned another date before leaving but I'm just prepping for this trip" Gave me the impression that he was kinda saying "I could have seen you the weekend before I left but I chose not to and prioritized other things" Sometimes I felt like the "what are you up to?" texts were because he wanted attention and validation more than his interest in me...

Also the night before the trip he hit me with "Hey, what are you up to?" responded and asked him the same but he didn't get back for 24hr+ on his layover

This might be in my head though. When he got back from the trip he hit me with a "hey, how's it going?" again and responded with a "hey stranger! [what I'm doing in a flirty way] we talked for a bit and he asked me out for Sunday. I told him I have plans already but I'd be down to see him for HH later that week. He picked up on the change in energy and said "should I be taking a hint?" I said "I'd love to see you again but already made plans. actually I wasn't sure if you were into it still. which is okay too but I had a good time on our first 2 dates. I'd go out with you again :). He explain the timing of the trip was awk and he's still feeling it out but would definitely like to go out with me again too. I said Yeah all that totally makes sense. We're still getting to know each-other.

We've been chatting a bit over the weekend but there's no date planned

IDK if I'm being to harsh and I should now initiate date 3? If he does want another date I think I want to let him know how his texting style is throwing me off ...

I was thinking of saying: "Hey, hope you had a good day yesterday. Thanks for being patient :) Let's get together after work this week. Do you like to play pool?" was thinking a dive bar for pool

Or should I wait for him to initiate ... see if he's really all that interested. Worried he might say yes to me asking him out for date 3 just to be nice even though he's not all that interested