This is actually forbidden.
As background, building new items is forbidden because of the melacha of boneh. Rebuilding is somewhat easier but not that much. As R Daniel Braude (Learn Shabbos, pp. 292ff) explains
- fastening tightly (e.g., with screws, nail or glue) is forbidden min haTorah
- fastening loosely (e.g., attaching parts of an item in a way that they are not fixed or attached well and therefore easy to undo) is
forbidden de rabbanan because of the fear one may transgress the
- connecting or loosely attaching things that are always loose is permitted
- screwing in the horizontal bar of a bench (that had been used and disconnected before Shabbat) into its legs constitutes the Torah
prohibition. Loosely screwing it into its legs constitutes a Rabbinic
prohibition. Placing the horizontal bar onto its legs without screwing
anything is permitted
- screwing in an extra leaf in a table [which can be extended in the middle] constitutes the Torah prohibition. Adding it to a table
without screwing it in but in a way that it remain somewhat inserted
into the grooves constitutes a Rabbinic prohibition. However, fitting
the slate into a table in a way that it is never solidly inserted is
Your case seems to be the first two ones one, i.e., either one needs to screw in the top which is forbidden, or to put the top on the feet loosely which is forbidden because of the gezeira shema yetaken (OC 313:6 and MB 313:41), i.e., that one comes to screw in the screws.
Of course, consult your rabbi
before implementing anything you learn here.
PS. A table is somewhat more complicated than a bench because it might be building an ohel (a tent) but that is only if you plan to use the space below the top.