You'll not find a perfect answer for text messages. Apple's come the closest, as you can sync iMessage between phones / tablets / macs, but its not perfect.

For intra-team comm's you should look at Slack / Teams. Easy to use apps for all likely devices, lots of features to organize conversations, search history, share desktops and documents, etc.

Texts from customers are harder to deal with. Maybe get a bluetooth keyboard and keep it handy?