Poked around a bit, found the logs. Looks like this didn't install correctly. Pathing and/or daemon not starting? Any ideas on how to fix this?
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Log: ~/.config/Mullvad VPN/logs/frontend-renderer.log
[2022-05-24 17:38:41.234][verbose] Tunnel state: disconnected
[2022-05-24 17:38:41.272][error] Failed to update the location: No connection established to daemon
[2022-05-24 17:38:41.272][error] Failed to update the location: No connection established to daemon
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Log: ~/.config/Mullvad VPN/logs/frontend-main.log
[2022-05-24 17:38:40.714][verbose] Chromium sandbox is enabled
[2022-05-24 17:38:40.715][info] Running version 2022.1
[2022-05-24 17:38:40.791][info] Detected locale: en-US
[2022-05-24 17:38:41.233][error] Failed to check autostart file: ENOENT: no such file or directory, access '~/.config/autostart/mullvad-vpn.desktop'
[2022-05-24 17:38:50.794][error] Failed to connect to daemon: Failed to connect before the deadline