How to replace a color everywhere in PowerPoint

PowerPoint cannot find and replace a color across a deck. If a color was picked from the theme, changing the theme colors updates it on every slide. If it was picked with the eyedropper, typed in as a code or pasted from another deck, it is fixed to that exact value, and the only manual way is to change each shape by hand.

Check whether a color follows the theme

Select a shape and open Shape Fill (or Font Color for text, Shape Outline for lines).
If the current color is highlighted in the Theme Colors rows, it follows the theme.
If it sits under Standard Colors, Recent Colors or More Colors, it is fixed and will not change with the theme.

Change the theme colors

Windows: Design, then the More arrow in the Variants group, then Colors, Customize Colors.
Mac: Design, then the Variants menu, then Colors, Customize Colors.
Set Text/Background and Accent 1 to 6 to your brand colors and save the color set.
Everything that follows the theme updates at once, including the lighter and darker shades.

Fix colors that do not follow the theme

Go slide by slide and select the shapes with off-brand colors. The Selection Pane (Home, Arrange, Selection Pane) helps with stacked shapes.
Pick the matching color from the Theme Colors rows for fill, text and outline.
Use the Format Painter to copy a corrected shape's formatting to others.
Check tables and charts separately: they keep their own color settings.

Slides pasted from another deck

Slides pasted with their original formatting bring their own master and theme, so their theme colors differ from yours.
Select them, then Home, Layout, and choose a layout from your own master. Or paste with Use Destination Theme next time.

What the manual way misses

There is no list of which colors a deck uses, so near-duplicates such as #3CB6EB and #3DB6EA slip through.
A color picked with the eyedropper looks right but is fixed, so it will not follow a template change later.
Status colors such as red, amber and green should usually stay as they are, and a blanket change would hit them too.