liluzivert I am wondering if ever registering this phones ability to connect to cell towers
Your phone can make connections to cellular networks without a SIM. This is to allow emergency number calls. Airplane mode prevents usage of the cellular network. If you have a SIM with airplane mode, texts and calls over WiFi will work if supported by your carrier. No SIM and enabled Airplane Mode together prevents communications.
liluzivert I have been using Google play services on my main user profile.
Depending on your threat model this can be fine since you can disable Internet permissions for Play Services. If you have to have the Internet access for the apps then there is that obvious privacy concern that maximum-privacy setups will have.
GrapheneOS suggests running Play Services in an alternate user profile as you've likely seen, if you have serious concerns regardless then do it that way.
My setup has the default profile as just the VPN and app installer of choice, and everything else done as separate, for-purpose profiles. Since apps from the admin profile can be shared to others, I consider using it as a template which all the other profiles share. What you choose to do is up to you.
liluzivert At this point, is a complete wipe and reflash of the operating system my best bet?
Even if you consider doing this, a factory reset is sufficient, as the disk is encrypted and the decryption keys of the previous install are purged from the device.
liluzivert If so, what are some good alternatives to having a sim card besides using WiFi?
Running your phone in Airplane Mode allows WiFi only usage without cellular network access (note: whatever services your M(V)NO provides over WiFi will still work).
You could keep a separate device with a SIM card for phone number and texts. You could also use something like a portable cellular network router with your SIM card to carry and keep in a bag to access the internet over 4G-5G. Some users said they had routers they could send and receive SMS texts from and access via a panel or app but I have no experience with it. Using the router while powered on will make you visible on the cellular network, although, they'd see info about the router instead of what phone you use.
For Web traffic, you use a VPN and that is all they will see. They will see a captive portal/connectivity checker on first connect but this can be disabled in Settings -> Internet.
As for recent details about phones sending connections to Qualcomm, Pixel phones after the 6th generation aren't affected, so don't have concerns about it.
liluzivert And should Google play be an absolute no go even on separate profiles?
Depends on your own threat model, Google Play usage can be done either way you like. If you are seriously concerned just don't use it or choose a separate profile for selective usage. GrapheneOS doesn't bundle them for a reason.
The GrapheneOS documentation is comprehensive and could help you choose what you would want to do for your setup.