info on PS 2024 update and my OS 12.7.1

Hi -I've been using PS CC2019 for...well since 2019 I guess. It started acting wonky today so I decided maybe I should update. I clicked 'update' within PS CC2019 and I don't think it updated, all I have in my dock is the 2019 shortcut icon with a question mark over it. So I went to the Adobe CC website and clicked 'open' on the PS icon there and PS 2024 opens for me.

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SO my questions are:

1. Do I have this new PS 2024 on my computer or am I using the web-based PS? I sometimes have to work offline so I don't think a web based PS will work out for me.

2. PS 2024 says I need to update my macOS to 13.4 or later for maximum performance/correct operation but I only have available an update up to 12.7 macOS. Should I (if possible) use an older verion of PS and if so, how do I acquire this older version?

Thanks for any help.