How do I access the entire Photos library from within a draft email in order to select images to attach?

Have you made your Photos Library your System Photos Library? If there are several Photos Libraries on your Mac, you will only see the photos from your System Photos Library in Mail.

Open Photos, if it is not running, then go to the menu "Photos > Preferences (or settings)". In the General tab of the Preferences click "Use as System Photos Library", if this is not yet greyed out.

If you are using Cloud Photos on your Mac, you may want to check in the Photos > Settings > iCloud, if you have "Optimize Mac Storage" enabled. The Media Browser can only show you the photos that have been downloaded from iCloud, not the photos that have been optimised to save storage. If you are using an optimized iCloud Photos Library you have to force the download from iCloud by viewing your photos enlarged in Photos, before you can use them in the Photos Browser in Mail or other apps.

Try using "Attach" (with the little paperclip icon) rather than "Photo Browser." You can point that to Photos, and that may be better for your needs. And keep the search field in mind to help find an image in a large Library.

And, by the way, you should consider the power of using Albums. In a large Library, they really help the organization-- especially since a picture can be in more than one album without taking up any more storage space. I have a folder of albums by date and one of albums by topic. So I can see all the pictures of the Grand Canyon together or all the pictures of Aunt Ethel together, or I can look at the pictures of Aunt Ethel on the Grand Canyon trip. Very handy...

Use the "Attach" button in the draft email as Richard suggested but you know that all you'll get are the thumbnails of all the photos in the library. There's no organization to them. However, you can use the search box to search for file names, titles, keywords or People names.

I found the best way is to add a unique keyword to the photo(s) and then search for that keyword.

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?