How do I update my iPhone SE when it says 'up to date' but I can't download certain apps?

My phone won’t update

That is correct.

Your 1st Generation iPhone SE.....discontinued in Sept 2018.....has reached the end of the update road. No more updates will be available for that model, since Apple now classifies that iPhone as obsolete.

If you need to run a higher iOS version, you will need a new phone.

The reason it says up to date is because that is the iOS limit for your model specifically. For the latest models, the up to date iOS software being signed is 18.3.2. Also many app developers have already stopped supporting their apps on older iOS softwares.