For information I reported this issue in Feedback at:
As can be seen from my own experience, not every Dietpi installation suffers the issue. Three of my four DietPi installations already had the required libicu76 (for Trixie or libicu74 on Bookworm) library present and encoutered no issues with the Roon Bridge 2.71 update but one did not.
The one Dietpi (Trixie) installation that did not have libicu installed was probably my most minimal one with an exceedingly small set of packages installed - dietpi-dashboard, Samba client, Samba Server, ALSA for USB audio and very little else. The other three installations were similar but not identical. In particular, different audio drivers were employed.
It would appear that DietPi, in its most minimal form does not install libicu. However, it also seems that in three of my installations another package was present with a dependency upon libicu that resulted in it being installed.
Edit and root cause (for me):
It turns out that I was wrong about the packages installed on the Dietpi system for which the Roon Bridge update failed. It did not have the Samba client or server installed whereas the other three did.
Looking further, it appears that, on my Dietpi Trixie systems, samba-libs have a dependency on libicu76
Thus, for me, the issue was that my Dietpi installation did not include the Samba client or server packages. Installing the Samba client or server would have installed libicu76 as it obviously did on my other three DietPi installations.