Welcome to the forums!
After years of riding in saddles the colors of which I was not always thrilled with (ask me about that blue-green dressage saddle, go ahead), I am DELIGHTED to say that dying a saddle is not nearly as daunting a task as it seems.
I have tried with only minimal success various darkening oils/products, they all help re-saturate the color, but I don’t find they’ll really take a say, fairly orange saddle, to anything other than a somewhat darker fairly orange saddle.
Fiebings makes a great leather dye, very affordable (amazon, your local tack shop, craft store), and even their little wand applicator thing works great. I usually use a bottle a saddle for a couple coats (start light), but pick up an extra for touch ups or if I spill the first one . I usually deglaze with some denatured alcohol (also super cheap, at Lowes or wherever), but have not had any problems the times I’ve forgotten. I was honestly amazed how easy it was- somewhat awkward balancing the saddle and trying to not get dye on the entirety of everything, but despite having no idea what I’m really doing they’ve all come out looking nice.
I would suggest wearing dark breeches/full seats for the first couple of rides/couple of rides in the rain. I had minimal transfer, and I know nobody really sees your bum but that would ruin so many nice over fence photos