Google Calendar. I don't think you need gmail, but you do need a Google ID to use one.
First of all, look at
Google Families. This is how you can share accounts, Amazon Prime stuff, reading lists, children's reading, music, YouTube streaming, etc. It's not mandatory, but if you like it, set it up first.
Now go to calendar.google.com. At the left side of the calendar, you'll see "My Calendars" -- and if you've set up Google Family, there will already be a Family Calendar there. Click the "..." next to the calendar you want to share, or make a new one, select "share with specific people" and fill that in. You do need an email address, but not a gmail one. You decide if the shared person can just see it, or also modify it. This makes it useful for poker groups, soccer teams, etc.
One nice thing is that each user can set their own colors, and, I think, other defaults. So my "private" events are purple, and shared ones are yellow, but DW uses shades of green and blue. Touch W M or Y for week, month, or year views.
Google Calendars has notification capability, so it can send you an email or a text at any time before the event. (I think this is up to each person ... you setting a reminder shouldn't cause a reminder for whoever you share an event with.) The calendar shows up on my Android phone, and somehow Alexa knows about it too. She can answer "Alexa, when is my appointment with Dr Smith?" When certain sites like hotels send you a confirmation, you can have that automatically entered on your calendar. (Truth be told, I don't remember setting this up -- but I like it anyway.)
You can use it to schedule events and invite others to them.
Accidentally-deleted things can be recovered. You can search for events in the past and future, so it's possible to use it for a billing record (I do that).