Hi and welcome.
Not sure what to advise (besides posting the garuda-inxi thing), but I see I have both of them, with PulseAudio provided by the pipewire-pulse package and not running. Excerpt from mine:
Audio:
[...]
Sound Server-1: ALSA v: k5.19.13-zen1-1-zen running: yes
Sound Server-2: sndio v: N/A running: no
Sound Server-3: PulseAudio v: 16.1 running: no
Sound Server-4: PipeWire v: 0.3.58 running: yes
(Yes I should update, there’s PipeWire 0.3.59-2 now)
I’m almost sure it did so by itself, or maybe there was some announcement or advice here time ago which I don’t remember. And sadly I don’t understand much of this as good as I’d like, so… 
Try searching around in this forum for “pulseaudio pipewire”, “microphone pulseaudio”, so on.
Maybe this?
pactree -r pulseaudio
fish❯ pactree -r pulseaudio
pipewire-pulse provides pulseaudio
├─easyeffects
├─gnome-bluetooth
│ └─blueberry
└─pipewire-support
pactree -r pipewire
fish❯ pactree -r pipewire
pipewire
├─fluidsynth
│ ├─calf
│ │ └─easyeffects
│ └─gst-plugins-bad
│ └─gstreamer-meta
├─gst-plugin-pipewire
│ └─pipewire-support
├─helvum
├─obs-studio
│ └─wlrobs-hg
├─pipewire-jack
│ ├─ffmpeg
│ │ ├─chromaprint
│ │ │ └─gst-plugins-bad
│ │ ├─ffmpegthumbnailer
│ │ ├─firedragon
│ │ ├─gst-libav
│ │ │ └─gstreamer-meta
│ │ ├─mpv
│ │ │ └─celluloid
│ │ ├─notcurses
│ │ ├─obs-studio
│ │ ├─qt5-webengine
│ │ │ ├─freecad
│ │ │ └─iaito
│ │ └─wf-recorder
│ ├─ffmpeg4.4
│ │ ├─opencascade
│ │ │ └─freecad
│ │ ├─vlc
│ │ └─wf-recorder
│ ├─fluidsynth
│ ├─gst-plugins-good
│ │ └─gstreamer-meta
│ ├─mpv
│ ├─obs-studio
│ ├─pipewire-support
│ ├─portaudio
│ │ ├─fluidsynth
│ │ └─libopenmpt
│ │ └─gst-plugins-bad
│ └─qemu-audio-jack
│ └─qemu-full
│ └─grub2-theme-preview
├─pipewire-pulse
│ ├─easyeffects
│ ├─gnome-bluetooth
│ │ └─blueberry
│ └─pipewire-support
├─pipewire-support
├─pipewire-v4l2
│ └─pipewire-support
├─pipewire-zeroconf
│ └─pipewire-support
├─qpwgraph
├─wireplumber
│ ├─gst-plugin-pipewire
│ ├─pipewire-alsa
│ │ └─pipewire-support
│ ├─pipewire-jack
│ ├─pipewire-pulse
│ ├─pipewire-v4l2
│ └─xdg-desktop-portal-wlr
│ └─xdg-desktop-portal
│ ├─imhex
│ └─xdg-desktop-portal-wlr
├─xdg-desktop-portal
└─xdg-desktop-portal-wlr
Note that I’m on Sway and I installed many other packages, so you may see a different output, but you get the picture: stuff depends on both of them. (pactree is in pacman-contrib).
As far as I can tell, PipeWire is “the way forward” and PulseAudio still there for compatibility with some things that depend on it, but has to be the pipewire-pulse one to coexist (and it depends on pipewire anyways, I surmise it’s a compatibility layer much like XWayland is for X11 on Wayland).
pacman -Rdd, as you probably know already, means “remove it even if it breaks dependencies” and, well, something broke indeed.
If you have a snapshot from before trying to remove any of them, I guess you’d be better off restoring it and proceeding from there.
If not, I’d try reinstall pipewire and pipewire-pulse and reboot with my fingers crossed then do a garuda-update for good measure and reboot again.
In either case, garuda-inxi will tell you (and those who may help you, if you post it) whether they are running at the same time (they shouldn’t) which would be a likely cause for the microphone problem. By the way, it’s probably useful to know whether it’s an internal laptop mic, or plugged in the sound card, or rather a USB or Bluetooth one.