If you want to prevent SMS from being used, remove the recovery phone number and/or 2-step phone number from your account. That's how I've had my account set up for many years, to prevent SIM swapping attacks. Just make sure you set up all the other 2-step options.
I did it on the account mentioned in post (didn't set TOTP though), and Google locked me out saying "You're entering correct password but we're not sure it is you. Try again later". And I tried and tried and tried, for a few weeks.
Then, after 2 months, I tried logging in and suddenly it worked.
I would start looking at the networks you are using. You may be unknowingly sharing your public IP or IP block with compromised machines that are part of botnets, which makes Google (rightfully) very suspicious of logins coming from there. I would also definitely get several hardware FIDO2 security keys as Google will likely trust those more than other forms of authentication.
That was on my company office network that had a stable IP address for I think a decade. Thing is, Google is now known to randomly become very paranoid and protects you from yourself, and, coupled, with complete absence of any support, often results in full account loss: you have better chances of speaking with the Prime minister of Estonia by calling their office than reach someone from Google.
How certain are you that none of your printers or visitors' laptops or whatever were ever compromised by a botnet? Or that your ISP isn't also serving customers who are compromised or malicious on IPs adjacent to yours?
A few hardware security keys will probably prevent this problem for you. I'm wondering why you didn't consider getting them after you had login problems before.
I don't really think hardware keys (which I have a few, btw) really improve security:
I use a seriously backed up password manager that I have means to access from anywhere, and the only thing I have to worry is that I'd forget my really complex password to access it, because it is unfeasible that I'll lose all my devices where it is backed up and also an off-site backup of it.
With hardware keys, however, I constantly have to worry to keep them with me or in a safe place and not to lose them.
(my position is partially rooted in the fact that I happen to live in a country where you can easily have all your material possessions forcibly taken from you)
This is about proving to Google that you're secure. Google doesn't know if the password you entered came from a password manager or not. But if you're using a hardware key, they know it's secure.
If you lose your hardware keys, you still have your other 2 factor options, so you are no worse off than your current situation.
Thing is, history has shown that nothing is reliably enough for Google, once it flags you suspicious. You've entered password and totp code? Nah, you're still suspicious. Gave one time backup-code? Hah, still suspicious. Have a hardware key? Nice, but you know you are really suspicious. How else can you prove that it's you?!
Does this remove the full screen popup that occurs on both my phone and tablet when logging into my Google account? I'm not sure what type of 2FA this is called, but I would like to remove it and have it directly ask for the TOTP.
When my bank introduced the option to use TOTP codes instead of SMS for 2FA, I said "Great!" and enabled it immediately. Unfortunately they don't let you remove the other 2FA options. So logging in, I now get three options for 2FA: SMS code, emailed code, or Authenticator code.
The safest option is a hardware security key because it is not vulnerable to phishing. And I expect Google to trust it above all other forms of authentication because of that. So anyone who is worried about losing access to their account should immediately buy multiple hardware security keys. You don't have to buy them from Google.
So we are at a point where just a strong password stored in memory is actually the safest option (given brute force protection)?
The safest option is straight out of 1994: Sticky notes.
Security keys can get lost or stolen. If someone breaks into your house or office, they're going after something other than a sticky note in your desk.
Passwords on sticky notes can be phished. They can also be lost or stolen. The advantage of security keys is that phishing doesn't work on them. Phishing is a lot more likely for the vast majority of people than a thief both stealing their security key and knowing what to do with it.
