Major point up front: I *hate* phone tag.
Big difference between personal and business phone etiquette. Business is pretty much the same as it has always been, and my office calls are always forwarded & show as such on my cell screen, so I know to answer with my department name. Nonetheless, if I need to call a vendor rep about something that I know will take awhile, then I send an email request for an appointment for a phone call, so that we don't end up playing tag. I'm partially deaf, so my office voicemail tells callers to please send an email because I am usually not able to understand recorded calls very well.
For personal calls, I went to the "text first" option a long time ago, which again, gives me time to put my hearing aids in first if I don't happen to be wearing them. I have the voicemail option on my personal phone turned off, so I expect people to send a text or email if they don't reach me. My phone has a screening option that I use full-time; it instructs the caller to leave a message, but I'm listening. Scam/spam callers hang up as soon as the screening service kicks in, but real callers stay on the line, so I just pick up at that point.
Any physician that I or anyone in my family sees gets the office number added to my contacts right away so that I can see that it is the office when they call (I ask them to tell me the number they use for outgoing calls.) I also like to use the patient portal, so it's simple to just have them text me to check it for a message if I'm waiting on something like test results.
I do not answer texts right away unless I'm actually in the middle of a texted conversation. I normally assume that texts are informational, and unless I'm in a situation where I expect timeliness (such as waiting for someone who is supposed to be meeting me within the hour) then I don't always check texts. I also have my phone set to flag closely-timed repeat calls and override DND for them, so my family knows that if they need to reach me even if they are not using their own phone or if it is the middle of the night, to call twice within 5 minutes and I'm guaranteed to pick up the second time.
PS: I use voice-to-text all the time. Simple way to get around typing out a long sentence.