How to Create a Button and Assign a Script to It Using Google Apps Script?

I’m building a Google Sheets add-on and want to create a button within the sheet that triggers a script when clicked. I understand that one way to do this is by drawing a shape and linking it to the script manually, but I want to explore if this can be done programmatically. I have three specific questions:

1. Is it possible to programmatically create a button (not just a shape) and assign an onClick function using Google Apps Script? If yes, how can this be achieved?
2. If I use the manual method (drawing a shape and assigning a script), will the button still be functional for other users when they install the add-on, or will they need to relink the script themselves?
3. What is the purpose of the SpreadsheetApp.getUi().Button method? Is this related to creating buttons within the spreadsheet, and how can I use it to meet my goal?

I would appreciate guidance or examples to help me understand the best approach for creating interactive buttons in Google Sheets with Apps Script, especially in the context of an add-on.

1. Yes. But not with drawing. You can use any external images as buttons. Use sheet.insertImage() and assignScript on the returned overGridImage.

2. Yes.

3. No such method. But you can use alerts