It is worth noting though that the show very much acts like its still in 2023. However there are problems with trying to squeeze a 2023 dating. As said before Spider-Man: Far From Home is set at the end of school and in the beginning of summer vacations, which ideally puts the setting in June-July. Again as said, in FFH, it is said the Blip occured eight months ago, and with FFH starting in June, it would put the Blip in October. Because Avengers: Endgame is totally set in 2023 (and not 2022), it forces Endgame to be set in October 2023, and FFH must be set in June-July 2024. With TFatWS, it is mentioned that at least six months passed since the Blip, which would put the events of TFatWS in April 2024 (or May 2024 for later events, if I am correct). This does enter into conflict with Bucky's assumed age, that is true, but changing the entire set of events to accomodate a specific age number, is sometimes problematic. Bucky is over 100 years old, and although he could certainly be aware that he is 107 years old, I don't doubt that, at a certain point, he kinda just digresses how old he is exactly, and ends up erroneously saying an age that he doesn't have. Assuming he momentarily got his age wrong isn't far fetched.
If one was to really try and accomodate the age of Bucky as much as one could, we could try and squeeze the Blip to early October or late September, and the six months later would be March, and there would be leeway to have Bucky's age correct... but it would then enter into conflict with the eight months later being set in June (maybe setting it on May?), unless that again is a miscalculation on FFH.
So overall, the evidence contradicts itself. You can't have Bucky's age correct if you don't contradict FFH's setting and the eight month later statements as well as the six month later statement of TFatWS. As of now, Bucky's age is the only element, in this discussion, that contradicts the currently accepted setting, and given there is ways to explain it away, we can be confident that Bucky's miscalculation of his age is not heavily detrimental to a 2024 setting for TFatWS.