An effective way to deal with bad feedback is to discuss measurable facts not anyones opinions including yours. Ask them for specific details. What exactly were you expecting to see by now? Exactly how long do you expect the rest of the work to take? Exactly what is or isn't in scope for the first delivery? How much documentation are you expecting? If you drag them into objective facts not arbitrary opinions and you are doing good work then you will succeed. Your initial question before edits indicates that you need to go back into the office and take a fresh, fact based, approach.
If you are at the end of a formal probation, and a panel has come together to assess whether the probation is successful, and they judged that they possibly made a significant error in the hiring process, then what is written as fine. After all in such situations it is better to be totally frank.
My answer assumes that isn't the case that they were giving formal feedback based on a review of a probation period. Had this been formal probation feedback I am sure your question would have been different (i.e, asked how to deal with bad probation feedback or having your probation extended). Another thing I am taking into account in my answer below is a one month probation is too short for a senior software engineer. Coding isn't, say, bookkeeping, where each months tasks are consistent, so a company needs to see a variety of tasks performed to be certain a person is, on balance, able to perform at the right level and is good fit for the team and role.
Outside of formal probation feedback the exact wording of what they said, taken as ad-hoc feedback, to a senior software engineer, is inflammatory. They could have just said ”we thought it would be bit further along” and that ”you have a lot of work left to get it to where it needs to be”. That would be a perfectly reasonable statement about their expectations of progress of work so far and judgement about the work left to be done on a specific task. Yet what they actually said was:
we don't expect you to know everything perfectly. Based on our levels
of conversation with you throughout the interview process, your code
submission, and your work history, we thought you were a bit further
along that what we're seeing so far. So we definitely have some work
to do to get you to that point.
To a native English speaker who has worked a number of global companies hiring and managing software engineers that reads as saying that you, not just this piece of work, are deficient. It can be very clearly read as implying that they think they have brought you in at too high a level. It implies that the company needs to train you to a level at which you can perform the duties expected of your role.
They could have said "I don't expect” and ”further along than I am seeing". That would have softened the statement a lot as it opens up the possibility that the person may have incomplete information such not knowing how mature or tricky to master the particular framework is. Yet they are making statements as "we" that given their seniority in the company can be only interpreted as being an official position.
I most certainly would have said ”I”, and not ”we”, when it isn't official feedback that hasn't been cross checked with other people. Also, having managed front-end, back-end and full-stack software engineers, I know how varied the work is, and how varied the maturity of front-end frameworks. So I wouldn't make a definite judgement based on one piece of work. Only if the person had claimed expertise of a framework during the hiring process, and was clearly completely unfamiliar with it when they started the job, would I be extremely negative based on one piece of work. You have very clearly stated you claimed no experience with this framework. The rational thing for a probation panel to do in this situation would be to extend your probation, and give you a different task, to see if there wasn't some extenuating circumstances so far.
As you are new to the company it is entirely understandable that you are taking that specific language as very negative feedback. If you believe you did reasonable work given the circumstances, and that you are being judged as not at an appropriate level of general technical competence, when you believe you are not over-promoted into this job, then it is rational for you to be considering all options. They even say that they thought you interviewed well, you submitted a test coding task, and you have a solid employment history. This implies you have reason to think you are not under qualified to work on this task. Yet getting defensive won't help. More objective discussion and transparency of the details will.
At this point in time you will be feeling singled out. If you are correct that this ad-hoc feedback was harsh the you might expect to learn that this person has a reputation within the company for making people feel defensive. In which case you might at some point see this particular point in time as a "rite of passage" into the company that everyone has to face.