How to render the content of a variable in a different template with Django?
I think your challenge will be in storing the data client-side until the client wants to view it. There are plenty of ways to do this with Javascript (Vue JS is a good option), but you'll have to get creative if you're trying to do it completely in a template. I can think of a few of options:

Avoid a Second Template: Would it be possible for you to populate a hidden DIV element with the second set of data, then simply have a button to toggle the visibility of that DIV? That would be the easiest, but perhaps it would not look nice for what you want to achieve. If you use Bootstrap to make your template highly responsive, you can certainly achieve this.
I'm not sure where your data is coming from, but it might be simpler to just re-compute in Python to generate the second template. Unless the data is in the megabytes, your client likely won't notice a huge lag, especially if it's opening into a new tab.
API - If you aren't already using Django Rest Framework, it will add a whole other layer of complication to the project. However, this will allow you to get far more creative with how you display your information. You can always take a hybrid approach where most of your stuff is still rendered by Django, then build a few API endpoints for that stuff which really needs them.

I'm quite the novice at Python, Django, Javascript, Postgres, and Vue JS, but by learning just enough about each of them I can see how I'll be able to accomplish most of my design goals, even if I have to constantly look up the code. I love how straight-forward Django's templates are, but when I shifted to DRF and Vue, I gained far more flexibility (albeit with far more complexity).
I have a button that generates a report in two variables: one has a short version of the information and the other contains a detailed version on it.
The view renders the information of the short one with a template, let's call it template one. I need to place a button in template one that allows to see the content of the second variable in a different template and also in a new browser tab.
Since the information is not stored in the database (so I cant' address it with ids) how can I pass the variable that contains the detailed report information (hundreds of rows)?
Is it okay to try to pass it using the template tag 'url'...? (It feels like a wrong approach)