Yes you are correct about 'operation of law'. The council cannot 'grant' you - or anyone else - a tenancy of the property if you have already succeeded to it, nor can they 'refuse to grant' one.
So I am not sure that I follow your last questions.
If you have a tenancy, you have it, regardless of what the council's records say. But obviously there may come a time when you would need to prove it, so it would be desirable to have proper recognition of your status by your name appearing on the documents and the council's own records, if that is what you mean by requesting a tenancy now.
You could ask the council to acknowledge that you are the tenant, and if they refuse, take them to court asking for a declaration about your status.
But this, of course, might just remind them about the 'window of opportunity', and tactically it might be better to hold back from doing this until the date has passed and the window has closed.
It is possible that the points system for bidding would play better in your favour if you are recognised by the system as being an existing tenant, but this depends on the individual system. You might want to seek specialist advice from Shelter or your solicitor about this.
As to your rights if they took you to court. If you have succeeded to the tenancy, then you are a secure tenant, and you can only be evicted if the council prove one of the statutory grounds under the Housing Act.
These include rent arrears, bad behaviour, etc etc, but they also include a specific ground for eviction where the tenant has succeeded and has been given notice of under-occupation within the specified time period (and suitable alternative accommodation has been offered). So, as the council have admitted your right to succeed, your status in court proceedings must be that of a tenant.