For Calendar:
For bluetooth: GitHub - blueman-project/blueman
As for Maps:
My suggestion is:
https://wiki.openstreetmap.org/wiki/Cruiser
To check more map viewers there is the following page
https://wiki.openstreetmap.org/wiki/Ubuntu
Gnome System Monitor replacement
xfce4-taskmanager
https://docs.xfce.org/apps/xfce4-taskmanager/start
For Cheese:
guvcview
http://guvcview.sourceforge.net/
Is GNOME-Maps primarily used for the Linux phones, because it would make more sense to not have it on the desktop version of Ubuntu Budgie, because most people unless they have laptops with mobile data wouldn’t be really utilizing the maps application.
The image is libadwaita on Endevour OS Budgie . What are termed legacy apps do have a custom theme applied, but not system settings or calculator. You can also see the latest default appearance setting for upcoming Gnome versions. 
mate-system-monitor was forked from GNOME System Monitor in the early days of GNOME 3. It is maintained by the Mate Desktop team. The issue tracker is well managed and the Debian Mate Team quickly packages their stuff.
It doesn’t install that many mate dependencies - basically translation stuff.
Mate System Monitor does NOT play nice with Pocillo - however with a bit of tweaking (in git master of the pocillo-gtk-theme repo) the treeview headerbar is fixed in light styling and dark styling. Plays nice with Qogir and Arc theme. Materia does not work that nicely though.
My thoughts… We live/work in a web-centric world, do we really need a desktop maps and (stand-alone) calendar app? I’ve never opened the maps app, I head straight for the browser for Google Maps or Open Street Map and have never seen anyone do otherwise. The same goes for a calendar - people using desktop calendars are likely using them from applications like Thunderbird or Evolution, otherwise they’re accessing their (very likely) Google or Outlook calendar from the browser.
I use the calculator a fair bit, as long as it works with common themes (usually Pocillo or Qogir for me), I’m good with whatever.
For system monitor, just include Htop 
(joking, sort of).
Document Viewer - i.e. PDF reader is currently managed by Evince “Document Viewer”.
In progress upstream is a GTK4 port and it will be a libadwaita based app. Unknown when it will land - but currently has GNOME 43 milestone associated with it - so Ubuntu 22.10.
Thus looking at alternatives in the archive - most PDF readers seem to be Qt based - okular which is well maintained is a KDE based app - so not suitable.
Thus atril - which is managed by the Mate Desktop team is perhaps the best alternative (?) - disappointingly there is a huge backlog of issues and progress is relatively slow unfortunately.
So open to ideas here - I’ll mark atril as a replacement for evince for the moment
Sorry to repeat but…
https://linuxmint-developer-guide.readthedocs.io/en/latest/xapps.html
…wouldn’t be an easier path ?
thats irrelevant - those are not in the archive.
That’s not irrelevant : an effort already exists to provide predictable app’s in GTK, why not use / share it ?
And
https://packages.ubuntu.com/search?keywords=xapps&searchon=names&suite=all§ion=all
…wondering if it’s also Mate’s approach in that matter ?
I made it very clear my view on this - this is extremely important - and without volunteers any “what about this” is very irrelevant.
An effort already exists on that matter to avoid wasting your time…
Budgie’s not alone with this « problematic » I guess Mate and Xfce are concerned too. And Mint.
file-roller i.e. the GNOME Archive Manager is a Gtk3 libhandy app.
It is autoinstalled for Nemo - Nemo has a recommendation for nemo-file-roller which is its file-roller integration i.e. on a right click you can compress a file etc.
Looking upstream there doesn’t seem to be any current move to Gtk4 / libadwaita.
The Mate equivalent is called engrampa and basically does the same thing.
Given that there doesn’t seem to be a roadmap for file-roller and due to the nemo dependencies think we should just leave this be for the moment and just monitor future stuff.
If anyone is interested - I’ve created a nemo-engrampa extension if they which to use engrampa rather than file-roller - Add engrampa support - closes #356 by fossfreedom · Pull Request #451 · linuxmint/nemo-extensions · GitHub
Deja-Dup is our backup tool - it is well maintained by GNOME. The next version is libadwaita though.
There seems to be a real lack of choices in the repo - need something that covers both adhoc and scheduled backups - to both local and cloud providers.
… and TimeShift is not a backup tool for local stuff.
This is one area we need to carefully consider - for the moment this is one libadwaita app that we may carry forward.
I’d forgotten this tool until I started looking around . It may be way off the mark though.
I had a quick look at that. It is broken in 22.04 … easy enough to patch though. Needs a bug report on launchpad.
It isnt a simple interface as deja-dup and could be confusing for some.
It isnt obvious also how to backup to cloud providers like you can with deja-dup
There was a reason it fell out of favor, but i don’t remember all the details.
You’re right to present it as a system backup as first purpose though it’s also possible to backup $HOME through TimeShift. The choice to backup all $HOME content or only the visible data - excluding the hidden ones - is a very careful and interesting ability.
This is kind of an easy decision.
GNOME Screenshot manages capturing screen-scrapes. However GNOME have replaced gnome-screenshot with their own inbuilt mechanism - so I would expect GNOME to place the app into read-only archive mode i.e. mothball it soonish.
Team member Jacob and myself have created budgie-screenshot which is part of budgie-desktop itself and has been submitted upstream. This will replace GNOME Screenshot in budgie-desktop 10.7 i.e. GNOME Screenshot will be dropped as a default app install.
I’m confused… All these mentioned applications are already (22.04) breaking my theme. They are all dark, it can’t be changed, changing the theme has no effect. I do not use dark themes at all. I don’t like these dark themed apps, so I’m already looking for alternatives. Using the flatpak version is solving the problem for the moment, but that can’t be a permanent solution.
Regarding the Mate apps: Client side decorations are missing, this also destroys the system wide theming. It looks cluttered, not professional. Especially the Mate System Monitor looks very ugly. In my opinion, of course…
