The journal doesn’t seem to be very responsive. Ideally, journals that follow an email submission system should respond to authors’ queries as the authors have no other way of knowing the status of their manuscript. In fact, I find it slightly odd that the journal simply mentions that the manuscript is being processed, rather than giving a specific reply about the status, that is, whether it is with the editor, under peer review, etc. I think you should wait for some more time before sending the withdrawal email. Perhaps you can send another email after a week and specifically ask whether the paper has been sent for peer review. Politely explain that as an author, you are anxious about the status of your manuscript and would appreciate if they respond to your emails updating you on the progress of the manuscript. If you still receive no response after 3-4 weeks, you can send a withdrawal request.
However, note that you cannot submit your paper to another journal until the withdrawal process is complete as this could be considered as duplicate or concurrent submission. The withdrawal process for the manuscript will be complete only when you receive a confirmation email from the journal editor. In case the editor does not reply even to your withdrawal request, you will need to send multiple reminders and wait till you receive a reply. If there is still no reply, you will have to write to the journal saying that you will consider the withdrawal process complete if there is no reply within a specific time (set a deadline of 2-3 weeks). You can then submit your manuscript to another journal. However, make sure you write to the editor of the second journal, explaining the situation and providing the email thread about the withdrawal as supporting evidence to assure them that there was no intention of duplicate submission from your end.