How can I troubleshoot the slowness?

[RelatableQuery]

JellyFin is running in a docker container on my Synology Nas. I consume it though either the web interface, an andorid app or the JellyFin for Kodi addon.
In all three instances browsing is very sluggish. The Web UI takes 10-20 seconds to load, in Kodi it could take 30 seconds to show the content, etc.
Once the media starts playing there are zero issues.

Am I just impatient and spoiled by using a local library on Kodi, or are there some tweaks I can make to speed things up?

[bitmap]

Local or remote when accessing? Is there a difference in speed between the two when you access in-network vs. external? Generally a faster internal drive where Jellyfin is installed (i.e., not a HDD) will lead to faster loading and navigation. Ideally media is on HDDs while your Jellyfin install is on an SSD or NVME.

[RelatableQuery]

This is local only. I never access jallyfin outside the house. Would installing jellyfin to an SSD as opposed to HDD make a difference? It's currently running in a docker containers on whatever RAID setup Synology set up for my 3 HDDs.

[bitmap]

Yes an SSD will absolutely make a difference. however, those times are pretty high so it may not be a panacea for your issues. Even on crap internet with a solid signal it only takes several seconds for my home page to load when I'm remote. As for local/networked storage: there will always be a difference (read: increase in latency) when moving from locally-attached storage to network-attached storage. And with Kodi, it generally loads up a file index rather than a "streaming" experience.

You can post your Jellyfin log to privatebin.net if you want help taking a look, but it doesn't sound like errors are the issue. One more question: are your server (i.e., your NAS) and clients using WiFi?