This episode is bursting at the seams, and I'm not sure how well it really holds together. The titular giggle is only a factor in the story for the first act, and is almost dropped entirely when the Doctor and Donna get to UNIT. From that point on, the special races from scene to scene, barely stopping to catch its breath.
And dammit, it works, largely on the strength of the performances. Everyone is at their best, from David Tennant, to Catherine Tate, to Jemma Redgrave, to Neil Patrick Harris as the Toymaker. Tennant sells the Doctor's absolute dread of the Toymaker before the episode has really earned it, and just as ably sells the Doctor's weariness as the episode essentially hits a reset button on the era that started back in 2005. The eventual bi-generation, and the fourteenth Doctor earning his "retirement," feel well-deserved. On top of all of that, Ncuti Gatwa's Doctor seems fully-formed right from the jump.
All in all, it's very fun, and very watchable. As a stray observation, I noticed the line about how UNIT's computers are running Triad on this rewatch.
Overall, I think the 2023 Tennant/Tate specials were a big success. They served up three distinct "flavours" of Doctor Who - madcap romp, existential horror, and epic final battle, and it did it well. I don't know how well it plays to new viewers, but they were certainly a good way to "wrap up" the 2005 reboot era, and start the new one.