How long will the stored yeast last, and is
this a viable solution
People write books on the answer to this. But... The short answer is every yeast and method is different.
You can reuse (save the yeast from your fermenter). Peoples success ranges from a couple weeks to a few months if kept in the fridge. Room temp is bad on yeast, as is sitting in a fermenter for weeks. Some yeast lasts longer, some die off more quickly. Also, the higher the gravity the beer was, or the hoppier it was, the less viable the yeast cake will be.
You can "rinse" or "acid wash" your yeast after fermentation is complete. Storage time can improve a little bit when doing this, but its more work and involves more aseptic (sterile environment) work load.
When reusing, different yeasts will react/morph differently through multiple generations of reuse. If it's a blended yeast strain, never reuse it, you will never see the same ratios as the 1st generation was. You can either trust someone when they say they got great results through 10 generation, or keep it safe and dont go beyond 3 or 4.
You can also split your new yeast pack and build multiple starters. Maybe start with a 100ml or 200ml starter, then restart that at 1L or 2L. The starters will last as above.
You can go full potato and "slant" or "plate" your yeast. Storage can last a year (two if properly frozen with mineral oil or glycerin). More lab type supplies needed, very aseptic environment and practices, and to make use of your "yeast bank", you'll need 2 or 3 starter cycles (1 to 1.5 weeks) to build the culture back up to a pitch quantity of cells. This is what i've been doing off and on, with great success. Once I realized that a starter should pretty much be done anytime you want to guarantee yeast viability (or prove it dead before pitching), I figured slanting wouldn't be much more work. You can literally get hundreds of batches from a single yeast package and its all essentially "1st generation" (not reused from brewing)
Google all the terms above and keep in mind that no single video, opinion, or website is scripture. Find multiple sources for the information and interpolate as you deem proper.