Calendar entries read-only

The Birthday picked up for an entry in Contact Application shows up in Calendar.

Can edit the Event Time as presented in below image.

Though, am running Ventura 13.6 the latest and greater offering from Apple for Ventura

Is your Calendar perhaps a Shared Calendar and is Lock by the Original Owner ?

If not, perhaps updating to 13.6 may fix this issue

About the security content of macOS Ventura 13.6

If Not >>

1 - Restart in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

2 - Safe Mode will also eliminate Third Party Software, extensions and drivers from loading. It will only load the Minimum amount of Core Apple Processes to allow the the computer to function at a reduced Level of Performance 

3 - Does the issue present in this mode ?

4 - Sometimes a Safe Boot followed by a Normal Boot will just put things right.

Colin Shapiro wrote:

My problem concerns Birthday entries in the Calendar app (running MacOS Ventura 13.5.2).

The entries are generated from the Contacts app.

I want to change the alert time of these events, but when I try to do this, I get an alert "...unable to save changes to XXX birthday. The calendar is read-only."

I used to be able to edit these entries previously - is this a Ventura issue?

Is there some way to change the Calendar from read-only to allow me to make edits?

Where is this particular Calendar?

ref:

Show contacts' birthdays in Calendar on Mac

Add birthdays to Contacts on Mac

if no insight or resolve you can file a bug report /submit your Apple Feedback here: Product Feedback - Apple

Refer to original reply and all aspects within that reply is suggested.

Should all suggestions provided not work out

https://getsupport.apple.com/?caller=home&PRKEYS=

2 of 3 suggestion and thanks

On to suggestion #3