Your company should be well familiar with the visa situation if they have hired foreigners before. Since your contract ends in March, there is no basis for the Immigration Dept to issue you a longer visa. In other words, your contract is ends in March, so that is also when your visa ends. But really, extending contracts and visas is very common. It requires a visit to the Immigration Department out in Shinagawa, but its a fairly predictable, routine submission. Your company probably knows that the Immigration department only issues work visas for one year - at least initially. Once you have built up a history here of work, tax-paying, social-insurance-paying, etc... you will likely get issued visas for longer and longer.
For your company, its not really a gamble. If all the paperwork is in order, the visa will get issued pretty automatically. It may feel arbitrary to you, but it is not especially arbitrary for your company or for the Immigration Dept. It can be arbitrary if you have things in your past (drug convictions, etc.) that may gum up the works. But for most people, its just a matter of ticking the boxes. Actually, its more risky for your company to grant you a multi-year contract before they even know you. It is more comfortable for them to issue you a one-year contract, then see if you are a good fit for them and their students.
You shouldn't feel that you have to give up on permanent residency, and that you should start planning on leaving Japan. Why would you do either of these things if you want/expect to live and work here? In the worst case scenario you discuss with your new employer sometime early January 2022 about extending your contract, and they either say, "yes let's do it", or they say, "sorry Jack, we won't be extending". In the case they don't extend, you will have about three months to find a new job, which shouldn't be difficult with a valid work visa that lasts until end of March.