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On Android with Samsung S23 (not using Avalonia) here is the functionality.

1. First tap into empty textbox the cursor appears.
2. Second tap into an empty textbox the cursor AND selection handle appears and the Paste, etc. Context menu opens.

I think you are oversimplifying this a bit and the selection handle is useful user feedback in some cases. At least it makes clear where the cursor is.

On Android with Samsung S23 (not using Avalonia) here is the functionality.

1. First tap into empty textbox the cursor appears.

2. Second tap into an empty textbox the cursor AND selection handle appears and the Paste, etc. Context menu opens.

I think you are oversimplifying this a bit and the selection handle is useful user feedback in some cases. At least it makes clear where the cursor is.

I'm only able to show the handles on an empty textbox when you long press. This both shows the context menu and the handle. Tapping doesn't. Imho, there isn't a purpose of the handle when the textbox is empty, as no selection can occur, and context menu will still show with long press

In Samsung OneUI this is what I see:

Single tap:

Tap once, wait and tap again:

Edit: And a purpose of this might be strong user feedback in the UI where text input will occur. This is easier to see than a blinking cursor in some cases. I also expect that the selection handles and context menu are always shown together.

We probably need to know what is done in iOS as well.

Yeah. We need to check how iOS handles it

First tap into empty textbox the cursor appears.
Second tap into an empty textbox the cursor AND selection handle appears and the Paste, etc. Context menu opens.

On iOS:

1. First tap shows the cursor
2. Second tap shows the context menu, but not the selection handle
3. Selection handle only appears if field is not empty, and user double tapped on the text (long press only moves the cursor).

Some apps (mostly, messengers) actually select all the text on second tap as well. But it seems to be a custom behavior.

Flutter seems to use the android behavior(long press to show handle and menu) when using the material theme, and no showing when using cupertino(ios)

Flutter matching the host OS behavior seems correct to me. That could definitely be debated though.