Is it considered a hefsek to play with one's fingers or silverware or such while waiting for the challah to be passed around on shabbat, after the blessing made on it? Even though it isn't talking, it is an activity unrelated to eating bread.
I don't have any sources off the top of my head to corroborate this, but I would say it's not a problem. The whole problem with talking in between making the bracha and the concluding act of eating is that you are taking the attention away from the main activity of the moment - waiting for the bracha to be said. Although playing with your fingers is not related to this, as long as it's not disruptive, it should have the same status as adjusting your seat when you sit down at the table.
I did not find any sources which explicitly address this (which is itself somewhat telling), but we could try to construct a picture based on the cases that are discussed.
There are two parts to the question, as with all discussions of hefsek. 1 - Is this something you are allowed to do? 2 - Is this something that, if I have done it, will cause me to need to make a new blessing?
I think part 2 is easier to draw support that in your case you would not need to make a new blessing:
Rashi (Berachos 40a) s.v. טול ברוך, writes:
ואף על גב דשיחה הויא הפסקה כדאמרינן במנחות (פרק ג' דף לו.) סח בין תפילין לתפילין צריך לברך
(Summary) Conversation is a hefsek, as we say regarding Tefillin.
Rashi understands that the laws of hefsek from birkas hamitzvah can be extrapolated to Hamotzi (and presumably all birkas hanehenin).
By Tefillin, the Mishna Berura 25:29 cites the Artzos Hachaim (Malbim) that לכתחילה you should not interrupt by making gestures with your fingers or hinting with your eyes. But if you did, it would not constitute grounds to need a new blessing. Tapping your fingers, even very consciously and intently, is no worse than that, and tapping mindlessly is surely much better. Therefore, I think it is safe to conclude that you would not need to make a new blessing.
Part 1 is not as easy to support so directly. The discussion in the Shulchan Aruch only mentions hefsek of delaying (O.C. 206:3):
כל אלו הברכות צריך שלא יפסיק בין ברכה לאכילה. הגה: יותר מכדי דבור
and hefsek of actual speech (O.C. 167:6):
יאכל מיד ולא ישיח בין ברכה לאכילה ואם שח צריך לחזור ולברך
Minchas Yitzchok (7:9) adds humming a tune, and Sefer Birkas HaBayis (38:2) adds grunting or making noises to intimate alacrity or anger (basically, saying "nu?!)" As mentioned above, pointing or making eye motions would also be ideally prohibited. These all seem to have the common denominator of being related to communication in some way.
The Mishna Berura (Shaar Hatziyun 167:28) extends this issue to walking around.
No one seems to extend the issue to something done mindlessly, so that would seem to be okay. If you were doing it with serious intent, it is still not included in the list of things mentioned explicitly. Perhaps it could be on a level comparable to walking around, but in my mind it is less of a real "action" to just play with your fingers.
see משנה ברורה ס'רו ס''ק יב who says clearly so long as one did not talk after the bracha it is only a hefsek if he is מסיח דעת which means so long as he didn't start thinking about something else, and take off his mind what he is waiting for (or talk) it is not a hefsek and he does not (and can not) make another bracha.