Make the search feature remember the last search term

When reviewing code, I often am interested in occurrences of specific terms, so I want these be highlighted to inspect the surrounding code.

(For security audits, reviewing UI templates I'm mostly interested in code inside those templates. Dozens of files means dozens of times I enter "CTRL-F, {".

Current behaviour

1. ALT-↓, Enter to open next file with diff
2. For example "CTRL-F {"
3. "CTRL-G until end of file
4. "CTRL-w" to close file
5. ALT-↓, Enter to open next file with diff
6. For example "CTRL-F {"
7. "CTRL-G until end of file
8. "CTRL-w" to close file
9. ...

Expected behaviour

1. ALT-↓, Enter to open next file with diff
2. "CTRL-G until end of file, repeating my prior search for "{"
3. "CTRL-w" to close file
4. ALT-↓, Enter to open next file with diff
5. "CTRL-G until end of file
6. "CTRL-w" to close file
7. ...

Even better

1. ALT-↓, Enter to open next file with diff
2. "CTRL-G until end of file, repeating my prior search for "{"
3. "CTRL-G jumps to next file from folder diff pane
4. ...