Excellent outline, - yes, within the first 6 months the "republicans" assassinated over 250 opponents (including Sotelo), destroyed 160 churches and burned opposition party headquarters and newspapers... this was publicized at the time, in the west, yet how forgetful of facts modern progressives (leftists) are. Not to mention taking power, the Frente Popular took a page out of Hitler's playbook, invalidating opposition members in parliament, so they could obtain a working majority. They were no more legitimate in power than was Hitler's regime legitimate after 1934...
Anyway, it is good to see someone on an English speaking forum that knows what really occurred and how despicable the "republicans" were. Events after 1931 changed the world, nearly as much as 1914, - nothing was the same afterwards, - people today think only in terms of German fascism, but Germany's fascism was only more notable because it took hold of a powerful state, with the second largest industrial potential in the world, plus a society that was remarkably cohesive; Germans had great differences to be sure, regional differences, and hundreds of years of bickering that were manipulated by neighbors (A-H & France), but 1919-1927 unified Germans on key issues, as bitterness over an injustice has quite a unifying effect. The fact is that fascism and communism were on the world stage due to the chaos created by 1929 & 1931 (all of which was caused by WWI debt, Versailles and Central Banks, like the Federal Reserve), most countries in Europe were gripped by one or the other, - Spain's difficulties didn't start in 1936, but rather in 1931 where in five years they had a couple dozen governments and great violence. They were not alone, France was gripped by the same leftism, - all of Europe outside of a very few states, England most notably (where the conservatives took power after 1931 through WWII, - though they had little in common with 19th century conservatism they did bring stability...), were gripped by one tyrant or another.
As to the rifle and your question, not sure if i understand, but the G98 stock will not work, but a 98a stock would, though there might be some fit issues. I am not positive about the Polish K98, I have never owned one, but I suspect it is exactly like the 98a and is a small ring receiver, so a 98k or G98 stock will not do, - G98 and 98k are large ring receivers and small rings receivers like the 98a aren't easily adaptable to large ring stocks. The SS did convert 98a to 98k and i have seen G98's with 98a barrels mated to them, so metal wise much is interchangeable, but stocks are going to have issues.
I do not know the situation in Spain, but Polish K98 stocks are not hard to find here, or weren't, neither are German 98a stocks. But complete stock sets can be expensive, especially if they are nice. The stock looks like a total loss, no fixing that, with the contouring of the stock, but does the rifle fully match? I mean, you do not show the components well enough to see if they match serial number wise, - the bolt is obviously Polish, but does it match? Do the other parts? if the action is not fully matching, it doesn't seem worth the effort? But if it is a family heirloom then I understand the desire to spend more than its worth, but you will have to find a Polish K98 stock, or a German 98a stock, neither of which is difficult here, but mostly because the US imported many from Spain in the 1960's (which might mean they are elusive in Spain today?)
You might just try and find a front end and handguard, maybe on ebay or Gun Broker, if you can find the front end of a 98a (the forearm) and a handguard, you might be able to splice it to your sporter stock. It won't undo the contouring of the stock, but it would have a general appearance of what it should look like and keep it in the original stock (generally collectors do not separate original stocks, unless it is a total and miserable loss, it harms the rifles overall value), - but much depends on how much contouring was done, which is difficult to tell in your picture.