It is possible to blow out seals from the overpressure in the crankcase.
I believe if your crank main rear seal blows out and oil blows out that side it can flow up over the flywheel causing clutch slip, this would also explain the low oil pressure light. There could also be damage to the oil pump itself, Foaming oil does not lubricate or cool very well so it is possible that you may have damage associated with overheating or lack of lubrication such as damage to the cam bearings. Did you notice any smoke coming out the tailpipe? If you blew a rear seal that could explain the clutch slip, and low oil pressure, the low oil pressure would cause issues with the VVT functioning (adjusting the timing) if like a ford it has an oil pressure-controlled solenoid, the lack of proper oil pressure would prevent the VVT from adjusting your timing properly which would cause a rough engine. I am not sure of the procedure to check for a blown rear crank seal or if there is maybe some kind of drain/access hole in the housing under the flywheel to see if there is engine oil in there. If you blew a rear main seal and got oil on the clutch, you will need the seal replaced and you will need a new clutch as you can not clean the oil off of that material. When it slips do you smell anything burning? usually when a clutch slips you will smell it, has a nasty smell, hard to explain the smell, almost like burning electrical to me but others say it smells like rotten eggs. If it has that smell you might not have oil on it, if it smells like burning oil when it slips then you probably do have oil on the clutch. You will probably have to get it to a shop to at least get properly inspected to figure out the extent of the possible damage. See if you have oil on the plugs, again you should see smoke out the tailpipe if oil is pushed into the combustion chamber, maybe pull the valve covers off and inspect the camshaft bearings for damage. Overpressure can also cause physical damage to the pistons, can bend and break things. Hopefully, you do not have any actual damage to anything and just need to replace the seal and clutch. I do not know if a blown seal will cause low oil pressure, maybe the foaming can or if enough oil leaks out and you have low oil in the pan, do you still get low oil pressure after you drained and filled to proper level? and with the oil still at operating level?
Not sure what that repair would cost, I think a seal replacement is going to be in the range of like $900, pre covid so who knows now. The clutch I do not know, but they will already have the transmission out for the seal replacement so the only added labor is pulling the old clutch out and sliding the new one in, couple hundred I think for the part. $1400 U.S I am just guessing, conservatively. I hate giving money to a mechanic so I myself would probably try to tackle it on my own. I would think maybe could be done for under $300 for parts and replacement oil.
Side thought... You said the new oil was very dirty, Could that be another clue pointing towards the rear main seal blown out? you could have oil blowing back into the housing where the clutch is then all that clutch material over time collected in there plus all the new contamination from all the clutch slipping getting in that oil and flowing back into the oil pan, that stuff can not be good for your parts that need lubrication, is this material flowing into the bearings and piston walls that need smooth lubrication? is it causing damage to the surfaces, is it clogging channels the oil flows through, could it have been enough to have clogged your oil filter blocking and seriously limiting flow to the engine? you are going to want to replace that oil filter as well.