A date oriented folder tree makes sense. Picking whether the date schema is "estimated when was the photo made" vs "when was the photo scanned" show two of the axes that you can organize around when using a date folder scheme.
I mix those two organizational schema. When scanning a roll of film, I try to scan in the order that the negs are on the roll. I do my best-guess at estimating about when the last picture on the roll was made and date the roll to that date. I store the results in a date organized folder tree based on when the photos were scanned, and name the files based upon when I estimated the photos were made along with a sequence number.
So ... Let's say I have a few scans made in 2017, 2018, 2019, and 2020. Each time I import into LR, I organize the incoming files into subfolders named by date inside the year folders, so
2017
-20170104
-20170322
2018
-20180214
-20180702
-20181010
2019
-20190510
-20190829
2020
-20200103
-20200205
might be the folder hierarchy.
The file names I code with my estimated date of the film and the sequence number for an exposure on that film. So let's say that on May 10, 2019, I scanned two rolls of 120 film, one 6x6 roll that I took the last photo on somewhere about June, 1982 (because I saw photos from my college graduation at the end of the roll) and another 6x4.5 roll about October 2008 (because I saw the photos from a car meet that happens every year about that time at the end of that roll and I also noticed that there was a photo of my friend from Italy in the set and he visited in 2008). The scans are named this way using a YYMMDD-seq02 naming protocol:
820601-01
820601-02
820601-03
820601-04
820601-05
820601-06
820601-07
820601-08
820601-09
820601-10
820601-11
820601-12
081001-01
081001-02
081001-03
081001-04
081001-05
081001-06
081001-07
081001-08
081001-09
081001-10
081001-11
081001-12
081001-13
081001-14
081001-15
Notice how I used the first day of the month as the lead number in the exposure dates? If I scanned two rolls of film that were obviously made in about the same month on the same day, I'd advance the day of the month by one for each of them.
These fit into the above hierarchy in the 20190510 ("May 10, 2019") folder. Et cetera. Doing this gets the files organized nicely in the file system and named in an understandable way that relates to the exposures' date contents.
Then onto your question:
Also how does cataloging in LR work exactly? You just add tags to each scan so then you can search for something like "dog water fountain" and then have it pop up rather than going through the folders?
I want to avoid the use of the term "cataloging" because Lightroom uses the term catalog to refer to the entirety of the database file that contains the pointers to where the original files are in your computer's file system as well as all of each photos image processing parameters and EXIF metadata, as well as any IPTC metadata you add to each photo. The application includes another organizing tool beyond the underlying*computer file system and file naming structure as well, called Collections, which is maintained in the Lightroom catalog. There are also star ratings, color tags, and flags. You can see from just the number of organizational things that you have at your disposal that there are a vast number of ways to use Lightroom (and the computer file system) to organize your body of original exposures, your processing efforts, and the finished works.
The facility you're referring to is called "keyword" and "keywording" wherein you assign tags to each exposure, either one at a time or in arbitrarily large groups. And it is much as you suggest: You add tags to the exposures and then then use a search function to bring up everything that has a particular tag. You can consider tagging at any level of metainformation about the exposure ... location, type, specific types of content, colors, emotional keys, event names, etc etc. They're all stored in the database file and are quickly found and listed for you when you do a search. How well you tag your exposures will determine how effectively you can narrow down a search to deliver exactly what you're looking for quickly ... It's a learning process that I recommend experimenting with a lot.
Once you find the set of photos you want, you can mark them and/or put them into a collection for easy access and later use.
I hope this response has helped. I've been scanning film and organizing it for close onto four decades now. It's a big topic and there are lots and lots of different ways to do it, depending on what your level of motivation is and what the goals of doing it are.
G