iPhone 15 Pro Max stuck on “Update finishing in background “ after 18.4 update for 3 days

Since you have cropped your image from the top, the status of the iPhone is unclear.

If it’s been saying “Update finishing in the background” for more than 3 days, that’s not normal. It should’ve been completed within a few hours at most. 

1. If you're using a VPN, disable it and check if the error goes away. Go to Settings > General > VPN & Device Management and turn off any active VPNs.
2. Corporate iPhone Profile Check and Removal Guide
   1. Is this your corporate iPhone? Then please contact the system administrator of your corporate
   2. If it is your device, in that case, do you have any profile installed by your corporate/organization/enterprise/School Management?
   3. Erase the profile added by you If you have installed a profile on your own --> Install or remove configuration profiles on iPhone - Apple ...
   4. Please contact the system administrator of the organization who provided the profile to you
3. If you connect to Wifi, doesn't necessarily mean you are connected to the internet. --> Internet not available WiFi and Cellular … - Apple Community

first lets try a forced shut down.

rapidly press the volume up then volume down botton then keep holding the power botton until you see the apple logo.

If that doesn't stop the update then try downgrading IOS it could be a bug. Go to ipsw.me and navigate the site to your iPhone which in your case would be the IPhone 15 pro max and then selecting IOS 18.3.2 and downloading the ipsw onto your computer, once its downloaded open iTunes or finder whichever your mac uses for connections to your IDevice and plug your IDevice in, then hold the option key while you click on update which will pul up a finder page and you can select the ipsw file and let it do its thing. Make sure you backup beforehand incase something goes wrong. You may receive a warning confirming your choice to roll back the IOS to an older version.

This should clear the message you are receiving.