Created attachment 159930 [details]
Example file

Also in
LibreOffice 3.3.0 
OOO330m19 (Build:6)
tag libreoffice-3.3.0.4

I can't confirm with

Version: 7.0.0.0.alpha0+ (x64)Build ID: 8c8b3a4f83f67882b284ddc3b3fe10d3fe6dedf4CPU threads: 4; OS: Windows 10.0 Build 18363; UI render: Skia/Raster; VCL: win; Locale: de-DE (de_DE); UI-Language: en-GBCalc: CL

My results:
after step 3: Image moves to second page (a lot of empty space on page one, but I remember, you've reported this in another bug report)
after step 6: No change in layout

I can confirm this with LibreOffice 6.1 , 6.3 and 7.0, all on Linux/Debian10. I do have a bit of extra information.

1) I open the document with LibreOffice 7.0. That's attachment "2323 - As downloaded.png"
2) I click the photo of the cat, then I drag and drop the image behind the last sentence on page two.
2) Then I wait and do nothing for two minutes. I don't move the mouse and I just stare at the screen. Nothing happens. 
3) Then I move the mouse a bit over the text, but not over the picture. Nothing happens. (Well, the mouse moves. :-P )
4) Then I move the mouse over the picture, which is still on its "old" position. I don't click the picture, I just move the mouse over it. That's when the picture jumps to the third page. On pages one and two there's now a lot of empty space. That's attachment  "2323 - Cat was moved.png".
5) Then I save the document under a different name and close it.
6) I reopen the saved file. The picture of the cat is now on page two. The anchor is on the position where I had dropped it. There's no empty space. That's attachment  "2323 - Reopen document.png".

The picture of the cat is not on the position where I had expected it, but maybe that's because the image is positioned horizontally from the left / to the paragraph and vertically from the top / to the margin.

				~~~

   Here are the versions that I used:

Version: 6.1.5.2
Build ID: 1:6.1.5-3+deb10u5
CPU threads: 4; OS: Linux 4.19; UI render: default; VCL: gtk2; 
Locale: en-US (en_US.UTF-8); Calc: group threaded

Version: 6.3.4.1
Build ID: a21169d87339dfa44546f33d6d159e89881e9d92
CPU threads: 4; OS: Linux 4.19; UI render: default; VCL: gtk2; 
Locale: en-US (en_US.UTF-8); UI-Language: en-US
Calc: threaded

Version: 7.0.0.0.alpha0+
Build ID: 4d03bd252274308f64332e7c0523068c38ac684a
CPU threads: 4; OS: Linux 4.19; UI render: default; VCL: gtk3; 
TinderBox: Linux-rpm_deb-x86_64@86-TDF, Branch:master, Time: 2020-04-26_05:59:56
Locale: en-US (en_US.UTF-8); UI-Language: en-US
Calc: threaded

PS: I'm not a developer. I submitted a few bugs/reports myself and I'm trying to confirm the bugs that other people reported here.

Created attachment 160136 [details]
2323 - As downloaded.png

This is the downloaded document in LibreOffice 7.0

Created attachment 160137 [details]
2323 - Cat was moved.png

This is what I get after I moved the anchor of the picture, and after I hovered the mouse over the picture.

Created attachment 160138 [details]
2323 - Reopen document.png

This is what I get after I saved the document under a different name, and then reopened it.

Correction, step 2) should have been:

2) I click the photo of the cat, then I drag and drop the anchor (!) behind the last sentence on page two.

After this step I forgot to renumber the following steps, sorry!

Still present
Version: 7.4.0.0.alpha0+ (x64) / LibreOffice Community
Build ID: 4659fc2f0a7223a89446edff0b77e58758b5edf5
CPU threads: 4; OS: Windows 6.3 Build 9600; UI render: Skia/Raster; VCL: win
Locale: en-US (nl_NL); UI: en-GB
Calc: CL

If you move the anchor to page 2 in multipage view it doesn't respond. If you click inside the document relayout being triggered

Well single page layout does the same thing