Yup, sadly SFO doesn't smile on the rats very much due to its extremely melee centric and cavalry centric balance. I can't give much advice beyond try to "play around" the mod knowing that there's a focus on melee, cav and magic.

Therefore play melee or magic centric factions like Mazdamundi or the newly upgraded vampires. I'm about to do another run of Isabella Carstein myself. Gonna challenge myself by not just spamming 9 vampire heroes and actually trying to use their units somehow lol.

Skaven are not strong for their ranged units. In fact, I would say only Skryre can get away with focusing on ranged without severely castrating their entire economy.

SFO might not make Skaven objectively better, but it does emphasize their strengths and weaknesses as it does with all factions. In vanilla, Skaven are absolutely pathetic when used conventionally, and this is doubly true in SFO. Playing Skaven requires completely different tactics and even a different overall mindset. As an example, if you have an unstoppable doomstack plus a few cheap worthless armies, that doomstack is probably your weakest link because it's likely costing you most of your passive income, which could have been spent expanding the under-empire and making a dozen more cheap armies.
There are a few key things you need to understand in order to properly utilize the power of Clan Mors (and the other clans too):

-Skaven are, above all else, expendable. The only good Skaven is one that died in place of a more valuable Skaven. Don't overlook the 0 gold cost of recruiting Skavenslaves, as this is one of your greatest weapons. As long as you stay on top of food management, they are your most efficient unit.

-Flanking is the only way to win melee combat in most cases. Fortunately, you happen to be playing the faction that is by far the best at flanking. Menace From Below is unspeakably useful for this, as it can spawn a unit behind the enemy that is more than capable of dealing a lethal blow. Remember, it's always the flanking unit that deals the damage, so it's best to use a low-damage unit as the bait, preferably one with either high defense, or even better, high expendability. One of my favorite tactics against Dwarfs is using a front-line of literally just whatever is available, and then using Menace From Below to spawn Clanrats behind their ranged units, charge *through* them dealing some damage but more importantly disrupting their fire, and just going straight through them to charge the undefended hairy rears of the dwarf infantry, which by itself should all but obliterate their HP and morale, and also buy time for more units to flank them.

-Defeat is acceptable. I mean really, if you lose an army that costed next to nothing, and they lost even 10% of theirs, then their victory likely hurt their economy more than it hurt yours.

-Expand your Under-Empire first, and your territory last. Also, most Undercity buildings aren't worth upgrading past tier 1. A mix of food income, gold income, (choose one of those two per undercity) and tunneling, in addition to the vanguard deployment building and/or the additional uses of Menace From Below, will grant you a stable economy and some very nice bonuses to help you out in battles.