As @uhoh stated, there is a crucial distinction between what is in principle "observable" and what we have to-date "observed."
Also, you have to specify whether you're talking about biggest in radius or biggest in mass. For stars with very large radii, like the St2-18 system you've referenced, they often can't even constrain the mass! And when they are able to, they end up having pretty small masses, i.e. UY Scuti. Stars, especially high-mass stars, generally increase in radius as they age, but they lose mass as they age. So it's not surprising to find red supergiants with very large radii (because they're at a late stage in their stellar evolution) and with small masses. But the theory behind supergiant stars is very complicated and uncertain still, making mass measurements very very difficult (And thus are not usually attempted) since mass measurements require some kind of binary interaction or a well-understood model of the stellar atmosphere (which is lacking for supergiants as I understand).
Regarding what's "observable," keep in mind that this is a fast-changing landscape: for example, gravitational wave detections of intermediate-mass black holes suggest that they possibly form from core-collapse of super-massive stars (among other possibilities). And the link to the question "what is the size limit theoretically of a star" that you provided has many answers which explain how uncertain such a theoretical limit is for mass and for radius.
Regarding "observed" systems, you must take into consideration the error bars on mass measurements of stars. The largest observed star with a known mass that has respectable error bars is the Wolf-Rayet star R136a1. See here for a comprehensive list.
With that said, you asked,
How sure are we (in percent) that St2-18 is right now, in 2020, still the largest observed star?
Of course there is always the possibility that with a new survey with better resolution, larger field of view, etc... even larger stars may be in the universe. It's a zoo! We were surprised to find stars as big as St2-18, so why would the universe stop there, eh? There COULD BE SOME reason in principle that disallows larger stars, but the universe keeps providing bigger and bigger stars for us to ponder, so there's no reason a priori to assume so. Regarding the survey you're asking about in particular, the wiki article has a nice discussion explaining the great uncertainty in determining the radius of St2-18, i.e. do we rightly consider it as part of the cluster or not in order to make assumptions about its distance, etc...:
A calculation for finding the bolometric luminosity by fitting the Spectral Energy Distribution (SED) gives the star a luminosity of nearly 440,000 L☉, with an effective temperature of 3,200 K, which corresponds to a very large radius of 2,150 R☉ (1.50×109 km; 10.0 au; 930,000,000 mi),[a] which would be considerably larger and more luminous than theoretical models of the largest, and most luminous red supergiants possible (roughly 1,500 R☉ and 320,000 L☉ respectively). An alternate but older calculation from 2010, still assuming membership of the Stephenson 2 cluster at 5.5 kpc but based on 12 and 25 μm fluxes, gives a much lower and relatively modest luminosity of 90,000 L☉. A newer calculation, based on SED integration and assuming a distance of 5.8 kpc, gives a bolometric luminosity of 630,000 L☉ although the authors are doubtful that the star is actually a member of the cluster and at that distance.
Lastly, you asked
How are we sure that St2-18 was indeed the largest object within the given survey? Technically speaking, one would have to calculate at least the distance or lumnosity for each object of the survey?
I quickly looked at the survey report paper, and it seems that this is actually unclear. Keep in mind that they were surveying a few different clusters, the Stephenson#2 being only one of them. The tables at the end of their paper make that clear. However, they only list the technical properties, and do not even attempt to constrain the radii for all of these stars. So I'd take it with a grain of salt.