will updating from Mac OS XEl Captain to Mac OS Monterey mess up my photo albums ?

Would be more concerned with the Time Spread and all the many changes between El Capitan and Monterey.

With that, there have been 6 newer versions of macOS since El Capitan.

Would suggest doing a gradual upgrade rather than a Flying Leap to Monterey.

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the Apple Store where the download can commence.

Computer Qualify for the Monterey upgrade

macOS Big Sur 11 hardware requirements

macOS Catalina 10.15 hardware requirements

macOS Mojave 10.14 hardware requirements

macOS High Sierra 10.13 hardware requirements

macOS Sierra 10.12 hardware requirements

Tips Big Sir Upgrade Released Nov 2020

Tips Monterey Upgrade  Released Oct 25, 2021

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey supports only 64 bit and there is no workaround.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may require an update or upGrades to 64 Bit Version

Unless that Air is a 2015 model (see menu > About This Mac), it cannot upgrade to Monterey. If it is a 2015 model, reconsider Monterey as the operating system is huge, and will place enormous demand on the limited CPU/GPU and RAM resources. It will run like a dawg.

You are welcome and thank you too 🇨🇦

Do come back to the Apple Support Communities ( ASC )  in the future, if / or when additional questions may arise

If you are using iCloud storage for your Photos it wouldn't matter what Apple device you were using or what version of MacOS /iOS/iPadOS you are using.