The first thing to do is a Force Restart. It may take a couple of attempts to get the speed and sequence of the key presses correct:
- Press and quickly release Volume Up
- Press and quickly release Volume Down
- Press and HOLD side button until the Apple Logo appears. Ignore anything else you see on the screen during that time and it could take up to 15 seconds before you see the Apple Logo.
For your Battery performance, check your Battery Health at Settings > Battery > Battery Health & Charging > Maximum Capacity. If it is below 80%, then it needs replacing. You can also check the apps that are using the battery at Settings > Battery and scroll down to show the battery graph and the top apps using the battery. You can post a screenshot of this page if you wish.
Apps are usually updated much more frequently than iOS updates and by default will update in the background, so not as noticeable as an iOS update. Some of these updates have seen poor battery performance and especially noted with the Meta updates. These have been updated as many as 10 times in just the last month and even Google has called out Meta for an update causing poor battery performance.
For not receiving Notifications, it would be helpful to know which notifications you are not seeing. Is it specific to an app and is it consistent or just happen on occasion. Do you have a Focus setting preventing notifications that would be identified with a Focus icon on the top of your screen?
Also after any update, your files are going to be reindexed and the photos will be analyzed with updated object detection algorithms. This usually only takes about 3 or 4 days and depends on the number of photos. These background processes will use more battery power until they are completed and is best to have plugged into power.