To add Categories (Blog, Event, Product) in Squarespace, you can follow these.
Event Categories
#1. Hover on an event > Click 3 dots icon > Settings
#2. Click Options > Categories
#3. Enter a category name then press Enter on your keyboard (or type comma)
#4. To see all categories on the Event Page, you can hover on the Gear icon > Settings
Next, click Advanced > Manage Categories
Blog Categories
#1. Hover on a blog post > Click 3 dots icon > Settings
#2. Click Options > Categories
#3. Then you can add the Category here
#4. To see all categories, click on the Gear icon
#5. Advanced > Manage Categories
Product Categories
#1. Hover on a product > Click 3 dots icon > EDIT
#2. Scroll down a bit and click on Category
#3. Add a category here
#4. To see all product categories, you can click on the Gear icon
#5. Click on Categories. You will see all product categories. To edit/delete, just click on 3 dots icon