SUMMARY
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In the Search/Replace panel, if you position the cursor at the end of the search string and then press and hold Backspace, only one character is deleted. If you press and hold a second time it deletes repeatedly, as expected.
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STEPS TO REPRODUCE
1. Open Find/Replace panel.
2. Enter a string in the Find field.
3. Position the cursor at the end of the string and then press and hold Backspace.

OBSERVED RESULT
Only the final character is deleted.

EXPECTED RESULT
If you hold the Backspace key it should continue to delete chars until you release the key.

SOFTWARE/OS VERSIONS

Fedora 38
Using Gnome & Wayland but with KDE Utils installed to get Kate and Konsole, etc.
Qt Version: 

ADDITIONAL INFORMATION
Behaviour is as expected for the Replace field.
If you place the cursor mid-field in the Search field then Backspace repeat works as expected.