how do I get the Photos app to update

The Photos.app is a part of the system. To get a newer version of Photos you have to upgrade to a more recent system version.

I see, you have been reading a support document about the RAW support. Do you need RAW support for a new camera? The RAW support is also provided by the system. To get new RAW Support, upgrade the system.

If you upgrade to the most recent system version, macOS 12 Monterey, these camera models will be supported: Digital camera RAW formats supported by iOS 15, iPadOS 15, and macOS Monterey - Apple Support

Or what is the problem why you want to update Photos?

One thing you should know is that if you upgrade to Monterey any 32 bit application which you have will not work, only 64 bit apps. To find out which will and will not work download and use the free GO64 app.

Also your Mac may be too old to upgrade to Monterey. What model and year is it? This Apple document lists those models that are compatible with Monterey: macOS Monterey is compatible with these computers - Apple Support

macOS 12 has brought quite a few nice new features for Photos, you may want to upgrade at least to macOS 10.14 Mojave and Photos 4.

Before taking the jump to macOS 10.15 Catalina and beyond you need to check carefully the compatibility with your apps and additional hardware, also the codecs of videos. This upgrade is breaking all older 32-bit apps and drivers, also some older video and image codecs (About legacy media in iMovie for macOS - Apple Support)

And Photos 5 to 7 are very different from the version you are using now, for example the Moments are gone.

Photos is a part of MacOS. To get a later version of Photos, you have to update MacOS to the associated version.

For example - Catalina has Photos 5

Big Sur - Photos 6

Monterey - Photos 7

Mac OS Sierra was released in 2016. There have been 5 versions of the OS more recent than that:

10.13 High Sierra

10.14 Mojave

10.15 Catalina

Mac OS 11 Big Sur

and Mac OS 12 Monterey, which is the current one.