Thank you kindly for your reply, and your added info.
I understand that you seek a "global" Safari solution. I do not know of one, yet am no expert. Such a feature may or may not be currently provided.
If suggestions help:
Apart from customising the tabs, seems there are some display controls.
I don't know if anything there may assist:
Customize your Safari settings on iPhone - Apple Support
Eg: says:
Change the display controls for a website
You can hide the search field, switch to Reader, and more.
- Go to the Safari app
on your iPhone. - Tap
, then do any of the following:
- Hide the search field: Tap
, then tap Hide Toolbar (tap the bottom of the screen to get it back).
- See a streamlined view of the webpage: Tap Show Reader (if available).
- To return to the normal view, tap
, then tap Hide Reader. - See what the webpage looks like on a desktop computer: Tap
, then tap Request Desktop Website (if available). - See a summary of the webpage: If Apple Intelligence* is turned on, tap Summarize at the top of the page. See Summarize a webpage.
You can also adjust Safari settings in Accessibility settings. Go to Settings
> Accessibility > Per-App Settings. Tap Safari to adjust settings. If Safari isn’t listed, tap Add App, then tap Safari to add it."
The linked "customize" article at the top also has other tips:
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Re: "every now and then the toggle switches from Private to non-private mode while I'm swiping up from the bottom to switch to another app."
Perhaps there is some workaround that may be better than nothing.
Eg: Wondering if the ability to lock / unlock private browsing may sidestep the offending toggle:
Browse the web privately in Safari on iPhone - Apple Support
Eg: says:
"To allow Private Browsing to be locked, go to Settings
> Apps > Safari, then turn on Require Passcode to Unlock Private Browsing, Require Face ID to Unlock Private Browsing (supported models), or Require Touch ID to Unlock Private Browsing (supported models)."