The Android Q Beta brought limited dual-SIM support on board for Pixel 2 and 3 users who previously had to choose between eSIM and standard SIM. This feature does not appear to be finished at all, as the latest Beta currently disables physical SIMs when you try to add an eSIM.
The bug arises when you head to Settings -> Network & internet and hit the little "+" button next to mobile network. Your Pixel jerks for a moment and throws you back to the lock screen, saying you don't have a SIM card inserted. Upon unlocking, you're presented with the setup process for eSIMs that prompts you to scan a QR code from your carrier. Hitting or swiping back throws you into Network & internet again, with no option to reactive the physical SIM your device isn't recognizing anymore – tapping mobile network opens the eSIM setup process again.
Don't click that "+" button next to Mobile network in the left screenshot. Your SIM card will stop working, and you'll be greeted by the prompt in the right image.
The solution to getting a fully functional mobile phone again is actually pretty simple, but not straight forward. Click the search icon or bar at the top of settings and type carrier or operator, depending on your language. This brings up a menu where you can choose to use your SIM card again (or add another carrier). Once you click that, you're thrown back into the lock screen to punch in your PIN and voilà – your mobile network should be fully functional again. [Update: As pointed out in the comments, your mobile data might be switched off after fixing up your SIM card through this process. A restart should fix that.]
To fix your mobile network, click "carrier" on the left and then choose your SIM card on the right.
This should serve us as another reminder that beta software is never guaranteed to work reliably and can end up breaking functionality. If you value (and need) a reliable phone more than the latest and greatest features, you should always stay on a stable release.