Your own last line is the best lead in the thread and nobody picked it up. You said the shift cables sit right in front of the fill point, and the problem showed up after the gearbox oil was changed. On these 5-speeds the cables run to a bracket on top of the box, and a man leaning in to get a wrench on the fill plug will push, unclip or unbolt that bracket to get at it. Put it back a spline or a few millimetres off and you don’t get a broken gearbox, you get exactly this: one gate that fights you, everything else fine, no noise, no grind. So before anyone prices a clutch, look at the cable ends at the box, the rubber bushes where they clip into the bracket, and the adjustment. Ask him straight whether he moved that bracket and how much fluid went in and whether it came out the level plug. Half a litre short makes this box drag; GL-3 75W80 is the right spec, and thicker oil to quiet a notch makes it worse.
Two quick tests you can do yourself, no tools. One, engine off, gearbox cold, run it 1-2-3-4-5 and back with the clutch in and out. If every gate feels identical cold, the linkage is not the problem, the fluid is too thin when hot or the clutch is dragging. Two, drive it twenty minutes so everything is properly hot, park, engine running, and try 3rd and 4th again. Worse hot points at the clutch or fluid. Same cold and hot points at the cable adjustment.
The pumping tells you something too. If pumping the pedal sometimes frees it and sometimes doesn’t, you don’t have a clean hydraulic failure, but you do have a soft line that may still be holding air. At 90k bleeding that clutch line is cheap and worth doing before a spanner goes near the bellhousing.
And the price you quoted, 150 for the set plus 150 labour, is fair for that car and I would not spend it on a guess. Do the cable check and the hot/cold test first. If the shop comes back saying clutch without those two answers, ask them to show you the release point on the pedal. A clutch that releases properly and still blocks one gate while parked is not a worn clutch, and you’ll pay twice to learn it.
thanks for the feedback!
One thing, I am not really fully sure if it 100% started after gearbox oil is changed as I drove the car maybe for 100 miles before giving to the mechanic (just bought it few weeks ago). I only came across that while I started the next day in the morning, pushing into 3rd by mistake instead of 1st.
I have a bottle for bleeding so I tried to bleed as much as I could, more or less 1 liter of dot4 I used until I saw clear fluid and no airlocks while not letting it going to min level but I am not a real expert so it is possible that I havent bled properly.
For the tests: first one, they all go in fine without any difference or issues.
part 2, I also had 30 mile drive few days ago and checked it after that - car parked engine on, still exactly the same with 3rd and 4th while stationary.
Okay so interesting situation after talking to the mechanic. Mechanic confirmed that he didnt play with the cables, while now we were talking he checked them and they seem fine. He sees the situation as weird and not “normal”, and like I said I dont know if it existed before the oil change which I assume it did. We also bled the clutch fluid agan and it seems fine.
He called a few friends including a gearbox specialist and the feedback from the gearbox specialist that it is most probably the synchro for 3rd and 4th gears and he had quite a few of them he opened for synchros. However, I am confused. The recommendation is to drive and if it starts to bring the same problems while driving, then better go to a gearbox specialist and open the gearbox to change the synchro.
I know some people say it is normal behavior and I want to lean into that, but i also checked with some owners, they tried to go into gears while stationary and they dont have such issue. My main situation here is that I have 1 year warranty from the dealer that sold the car and maybe I can handle it with him or return the car ( I spent some money already, dont want to do it but an option)
I am already starting to not like the car, been quite unlucky with last purchases for myself while whatever I bought for the wife were tiptop 
You are misusing the transmission; you should not drive away from a standstill in third gear. Therefore, the ability to shift into third or fourth gear while stopped is not a concern and the warranty company will not have to pay for a transmission repair.
…will become damaged if you continue to force the shift lever into third gear while stopped.
it was just gear in and out, no trying to move the car - i have stopped it and only mechanic did it for test purposes today 
Anyways, i decided to drive it as it is, if it goes berserk for those gears while driving in the future will fix it accordingly, Thanks everyone for the support.
One thing worth doing this week, before that warranty conversation goes cold: get the dealer to write the fault down.
Book it as a complaint, have them road test, and get it on a dated service record: third and fourth baulk when stationary with the engine running, no grind, first and reverse clean. That puts the fault on paper inside their one year. Without the record, the same complaint in eight months is wear and tear, and the gearbox is your bill.
The specialist’s read is the one that fits. A dragging clutch blocks first and reverse worst, and yours are clean. A synchro that has lost its bite blocks only the gears it owns, hot or cold, and does it quietly.
Driving it is fine. Just do not force it, and if it starts grinding on a third or fourth shift at speed, stop there. That is the box coming open, and by then the record is already on file.
thanks mate, its more like a car trader actually, i already made written complaint to the their email early this morning and then called them, this is kinda small family company bringing cars from Germany.
I have explained all, awaiting for them to tell me what they want to do next. I also recommended if needed I can go to Mitsubishi dealer for written proposal (even if they say not needed I will do, to have proof like you said) and park the topic. If something happens within a year then I`ll pull them in, hopefully wont be necessary
Good. The written complaint was the right move, and the dealer’s written proposal is worth having even if you never need it.
Two things keep it alive: the date and mileage on the complaint, and the dealer’s own diagnosis written down with the fault named (3rd and 4th blocked at standstill with the engine running, 1st and reverse clean). If the gearbox gets opened inside the year, that paper is the only thing separating their fault from wear they can bill you for. A fluid top-up is not a fix, and don’t sign one off as one.