Interesting story, except for the fact that even in Japan, in-company rules like "no relationship between coworkers allowed" has actually been made illegal for almost 2 decades by now.
Manga and LN authors still loves to uses it as a way to forcefully pushes the characters to hide their relationship, but there are just better way to do it. (It's kinda ok for manga and LN from the 90's or even early 2000's when it was still not yet clear, but nowadays, that's just a 100% lazy setup.)
For instance, it could have been a simple rule of "No romance during work time." mixed with something like the will of the couple to not display their relationship to avoid pressures from coworkers regarding said relationship. (It's also no yet clear if Taiyou is wearing his ring at work which seem similar to his wife's ring on the few panel where he wear it at home.)
In certain prefectures, any business who Is found to have such a rule or even unofficially enforce such a rule can be fined for as much as 20 million yens per infraction. As such, any startup companies would just avoid such a rule from the start.
Japan is not crapping around with its extreme case of low birthrate and children-to-parents ratio. It invest billions of yen every year in various ways to try to raise the ratio. In 2019, for example, the Children-to-Parent ratio in Japan was as low as ~0.42 meaning that, in averages, more than half of the registered married couple doesn't even have a single children. Back then, a study among 20K students in famous Colleges and Universities pointed out that ~68% of the woman and ~54% of the men wouldn't want to get in any relationship anytime close and, instead, wanted to focus solely on their career for at least 10 years. And other studies shows that over 88% of the single people situated, in their life, at that "10 years later" with stable incomes/career aren't feeling any need to get into a relationship unless "the perfect" companion would knock at their door (meaning unless something happen without any efforts on their end because all their energy is still spent on their career) which, as many already knows it, it's less than likely to happen than winning a lottery that truly set them for life.
As such, if any business was to truly put a rule that would disallow coworkers from getting into a relationship while off-hour and if it would have been found out, the company would not only get hit by a fine, but might also get hit by quite a few cases of social degradation (being targeted and bullied by medias &/or social groups).
