that is quite a bit of fork oil, surprised you hadn't noticed it before. Either way, if its made it to your caliper, make sure it hasn't made it to your pads. I know isopropyl alcohol ($2 at shoppers) works well for cleaning up brake fluid, but I am not sure if it works for cleaning up fork oil. If it's made it to the pads, they may have soaked in oil, which means they will need to be changed. One thing to check before you go through the fork seal changing process, is to make sure the tube itself is not pitted or scratched. Given the significant amount of oil leaking, it is possible. If the tubes are scrached/pitted, no matter what you do it will always leak, a seal replacement will not stop it. Typically this is not the case though. Sometimes it can just be dirt, some old 35mm film or tools available online to run under the fork seal may help. I have never had any luck with them, and don't like the possability of pitting the fork tube, since you don't know what you might be pushing out.
If it is your fork seal, have a read online about opinions for your model. I tried aftermarket seals, only to re-do the job using pricey honda OEM seals, but they work well. The labour/effort is much greater than the cost of the seals. Depending on how technical you are, and if you have the service manual, a fork rebuild is on the (IMO) 7/10 skill level to do it correctly, bleeding the air properly from the tubes, getting creative to make tools to unload the forks, actually determining which way the seal goes, setting lock nuts and rebound adjustor ranges. Having someone around that has done it before is a very good idea. Just a hint, start unscrewing the fork caps before you take the forks off the bike, once they are off, the forks are round and spin, it is difficult to get grip on them without damaging the fork. A vice (used gently!) is very handy later in the process. For me, truck straps and some fabricated S clips to pull the collars down and load the spring to get the tube apart works nicely. Not as bad as it sounds, but it does take patience. Shops usually charge pretty good for this type of work, a solid service manual and some creativity can go a long way. If you do change the fork seals, remove, clean (sunlight + hot water), dry, and rebuild both forks if you haven't done it in a while or do not know when it was done last. One fork refreshed and one fork with old gunky oil means the suspension may not work optimally.