A lot of this is speculation that has been proven false already, or can be explained otherwise.
Gallop has been having trouble since ARC-V. It wasn't just VRAINS. It's more accurate to say they've been having problems for the past decade, not just the past seven years. A prominent animator under the username maiko_2222 even spoke out about how bad things were at the company towards the end of ARC-V's production.
With VRAINS, the problems at Gallop just became a lot more apparent and harder to ignore, especially as the series director left around 20 episodes into the series.
"Yu-Gi-Oh! SEVENS itself wasn't planned to be immediately put into production"? Did you forget the six month gap between the sudden end of VRAINS and the airing of SEVENS? Gallop having problems since ARC-V meant TV Tokyo and Shueisha (the actual rights holders of the YGO anime) had more than enough time to find a new studio for YGO post-ARC-V. I'm guessing Gallop's contract with them dictated that they work on VRAINS regardless of the situation of their company, but as it became apparent that Gallop was falling apart, TV Tokyo & Shueisha spent VRAINS' production and air time looking for someone to take on the 7th series.
Also, production on SEVENS was actually ahead of schedule and going just fine. One of the staff even tweeted that, when episode 3 of SEVENS aired, they were already working on episode 10. They were around 7 episodes ahead in terms of production.
But why was SEVENS so rushed you asked? Did something else happen that wasn't related to planning or working on things in 2020? Something that disrupted the entire world and forced SEVENS to take not just one but two hiatuses, therefore taking around 8-10 episodes away from the total?
The pandemic hit Japan a lot harder than it hit the US, mainly due to a combination of factors like slow response, outdated information, and the country’s infrastructure not setup for remote work. A lot of companies in Japan lost around 3-4 months of working time as they tried to adjust. Bridge wasn't the only company affected. Other anime airing in Spring 2020 also notably had problems, like Balance:UNLIMITED, as an example.
I have no doubt that they had other plans for SEVENS and that's why the ending of SEVENS felt so rushed. But they also lost around 3 months of time and probably had a pre-planned schedule with TV Tokyo & Shueisha for the delivery of the next series in April of 2022 that they could not deviate from. Having to re-draft an entire series mid-production because of lost time due to the pandemic is a job I don't envy, and for what it's worth, SEVENS was still enjoyable regardless.
The first two arcs of SEVENS, notably, feel a bit tighter than the rest of the series. This is because of how they probably wrote out the first two arcs before the pandemic hit, and then had to scramble after as they adjusted workflow.
(This is only tangentially related, but Bridge isn't really a no-name studio with no experience. The studio is made up of former Project Sunrise members, some of whom worked on shows like Cowboy Bebop and Code Geass.)
I do agree that Go Rush definitely feels a bit more cohesive, and I attribute that in part to the fact that they have a better grasp on workflow post-pandemic, not because Bridge has "more experience working on Yu-Gi-Oh” now. SEVENS could have been even better and amazing if it weren't handicapped by world events, especially since we already saw the makings of it in the first two arcs.
We knew they had the potential. It was just unfortunate a global pandemic happened.