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The Friberg AGNT gives the analysis of imperfect OR perfect but their ANLEX gives the lemma of the imperfect form (with the smooth accent) as στήκω.
Logos gives the analysis as imperfect OR perfect but chooses ἵστημι as the lemma.
BDAG seems to favour the perfect.
It seems that the choice of breathing by SBLGNT prefers the imperfect of στήκω over the perfect of ἵστημι.
Either way, it seems suboptimal to choose an imperfect analysis and ἵστημι at the same time.
I think this is almost certainly a perfect. στήκω forms as a back formation from ἵστημι derivatives are (a) uncommon, (b) mostly confined to imperfective imperatives, (c) late.
BDAG's judgment that it's perfect regardless of breathing seems to me reasonably grounds to stick with an analysis of perfect, and leave the lemma as is.
That's my take on it.