Is it okay to resend an email to a journal asking for the status of a submitted manuscript? This question is related to the question asked here: Is it okay to inquire about the status of a paper when the online submission system shows no update three months after submission?.

Around 4 months ago, I submitted a paper to a Math journal for peer-review through an online submission system. The same day I received in my e-mail an acknowledgement message saying that the paper had been received.

The status of the paper on the online submission system is still "Manuscript submitted", and the paper has not been assigned to an editor yet.

One month ago, I sent a polite email asking for the status of the paper, but I got no response.

Should I send a second email in the regular way (that is to say, not using the journal's online system)?

Is it possible that things go slower during this time of the year (due to holidays or something)?
Yes, you should definitely send another polite email. You could also write directly to the editor, since your situation sounds fairly unreasonable. You deserve some sort of response to your submission. I would consider withdrawing the paper and submitting it elsewhere if you don't get a response.