Bluetooth connection between iphone & Mac Studio

You cannot pair your phone and your computer if that's what you're trying to do. That's not how Continuity works. Yes, both devices need to have BT turned on. They also need to be connected to the same WiFi network as the transfer is actually done over WiFi.

See also:

Use Universal Clipboard to copy and paste between your Apple devices - Apple Support

jshaw6 wrote:

I still get the Pairing unsuccessfule Mac Studio is not supported message on my phone.

As I said, you cannot pair the two. You will always get that message. That is expected. It has nothing to do with your issue. Just make sure that BT is turned on on both devices then leave settings.

The first, simplest trouble shooting step is to restart both devices.

Grant Bennet-Alder wrote:

Is Handoff still turned on?

sometimes updates turn features off, and they need to be turned back on manually. And a restart AFTER any change may also be required.

Good point.

Is Handoff still turned on?

sometimes updates turn features off, and they need to be turned back on manually. And a restart AFTER any change may also be required.

I doubt an update is the cause. If it were, there would be lots of complaints here in these forum. I haven't seen any. And, it still works just fine for me. So, while you undeniably have a problem, I don't think that's the cause.

I saw above that you said you had the most recent OS. Is that on both devices. I believe I heard that there was an update to Ventura last night. You may want to check and see if that makes a difference.

Have you recently upgraded your iPhone OS?