What phone do you have?
Samsung Galaxy S7
I’ve experienced this on my old Moto G4 for some time and got use to it, but I see it still happening when I moved to an S7 that had fresh install of everything.
When I use the Anywhere App from a PC (happens more with group text) or sending a text message while talking with Google Assistant in the car, the messages don’t appear in the Anywhere app on the phone until I reboot the phone. If I send the message from the app on the phone, I see it on the PC right away.
I’ve tried the reset “Local Content” on the phone and PC many times, but it continues to happen.