In the stagflation scenario, higher interest rates would cause your unhedged stock positions to lose value due to PE contraction, but on the other hand you'd have the opportunity to buy investments on sale. If you have $1M in cash, then the middle of a stagflation episode is not a bad place to be. You'd get to ask yourself "Shall I buy treasuries yielding 7% or shall I buy the S&P500 at a PE ratio of 12 and dividend yield of 3%?" However, if you already lost half or more of your portfolio's cash value during the stagflation episode because you started with high-priced stocks and bonds, you wouldn't be able to fully capitalize on the opportunity. Chances are you'd have to go back to work while agonizing over the knowledge that the 30-year safe withdraw rate is probably 5-7%, but that's a lot harder to prove than the 4% rule.
In the severe recession scenario, expect stocks to drop another 20-40%. This is a similar setup as the stagflation scenario, except in the recession scenario bond yields will likely fall. As in the stagflation episode, this would be a great time to buy if you haven't already lost much of the value of your portfolio! Also, recessions are the perfect time to FIRE with a higher-than-advised withdraw rate.
To summarize these ideas, if you think either stagflation or a recession is probably on the way, capital preservation should be your first concern. In either scenario, a big stock sale and much higher SWRs are right around the corner. The right things to do in either case are to (1) raise your allocation of cash, and (2) aggressively hedge or otherwise reduce your exposure to stock beta.
It's not that the recession or stagflation are bad for you in and of themselves. Your ability to capitalize on these future conditions depends completely on whether you lose a large chunk of your portfolio prior to the big investment sale.
Also, in the stagflation scenario, it is important to take steps to reduce your personal exposure to inflation. A home with a long mortgage, solar panels, insulation, a highly fuel efficient and durable car, the ability to fix things instead of replacing them, a low "electronics" footprint, preferences for free entertainment, a lack of booze/cigs/drugs habits, getting plenty of exercise, a preference for low-processed or no-processed foods, a preference for quality furniture and household items, and cheap hobbies go a long way toward preventing your spending growth from directly tracking CPI. These behaviors break a key assumption of most FIRE models which limits the SWR.