Auto Capitalize New Sentence in Mail

Just to be sure, you've checked

System Settings -> Keyboard -> Input Sources -> Edit

and confirmed the capitalization option is turned on? If so, have you tried toggling it off, clicking Done, and then back on again?

You can send feedback to the Mail product team requesting that initial capitalization be enabled, but otherwise, without a little third-party app help, you won't get initial caps of sentences without the Shift key.

There is a free application in the Mac App Store named WordService. It provides an Initial Caps of Sentences service, among many others. You would enter all of your email body, select it, and then from the Mail Services menu, you would select WordService: Initial Caps of Sentences and every selected sentence would have its first letter capitalized.

When you download WordService from the Mac App Store, that process will automatically install the services but not activate them. So, on macOS Ventura or Sonoma, you would do the following to activate Initial Caps of Sentences service:

• System Settings > Keyboard > [ Keyboard Shortcuts… ] > Services > Text
  • Scroll downward in the preceding Text window to locate WordService: Initial Caps of Sentences, and click the preceding box to enable it. You might also consider Sort Lines Ascending/Descending services for sorting text lists in documents.
• In the Mail compose window, you select all of your entered text, right-click, and choose Services > WordService: Initial Caps of Sentences.

WordService also installs an application of the same name in your Applications folder. When you launch it, a PDF document opens in Apple's Preview describing each of the installed services.