In general, with pickled items we can many of them to make them shelf stable, not so much to kill the botulism. There may be a few things that the heating adds some additional security with, like if the final Ph was a bit higher than intended, but mostly the vinegar does the job as long as you are getting it to the right levels.
Now, next question is, how long are they then safe for under refrigeration? This article https://www.eatbydate.com/other/condiments/how-long-do-pickles-last/ seems consistent with others I could find. It is referring more to commercial product after opening, but home made to proper standards I would think would be similar. They state that refrigerator life after opening, with proper storage, is similar to original shelf life of canned, 1-2 years beyond commercial "best by" date. Now, yours are home made, so you did not open them and don't have some best by date, but I think it would be safe to say treat them as an opened item which has already reached its best by date and error to the low side. If you like them, use them within a year. If you do not use them within a year, meh, must not have turned out the way you wanted, so toss them and try again.
What is proper storage? There might be a could points I am missing, but generally, make sure they are not contaminated by other items. Make sure the item stays fully covered by pickling solution. Make sure lid is in place and clean when putting back in the refrigerator. I would discourage removing product and then putting left overs back into solution. Such things might not be high risk, but do introduce some risk in contamination and defeating your pickling protection, and will deteriorate quality even if they do not cause illness. The pickling solution can only protect if the product is in it though.