[Avodah] Mourning for the Temple or repenting?

[Akiva]

Mordechai Torczyner wrote:

>>However, perhaps another root of the bein hametzarim practices is a
fulfillment of Zecher l'Mikdash, which the gemara (RH 30a) traces to "Tziyon
he, doreish ein lah" - we are obligated to be doreish (to seek out) Tziyon.
Of course, zecher l'mikdash could also be external and action-based, but the
concept of being "doreish" sounds stronger than that.<<

You're confusing zecher lemikdash with zecher lechurban. The former is marking mitzvas that were done while the BhM stood and include things like lulav kol shiva. It is with respect to this aspect that the gemora uses this posuk. Furthermore, there is no element of aveilus involved; lulav is performed publicly on YT, and many more proofs.
The other zecher is an aveilus type zecher and exists WRT the events of the destruction. It is not here that that posuk is used.

Akiva