The short term relationship between stocks and bonds is a fairly complicated on. Over the longer term both asset classes thrive in disinflationary environments. Bonds also do even better in outright deflationary environment whereas stocks don’t.
Both tend to struggle in inflationary environments whilst stocks can tolerate mild inflation, but both get clobbered in highly inflationary environment (don’t believe those those say that German stocks thrived during hyperinflation, they are full of shit).
But despite whatever the prevailing macroeconomic environment, bonds do have a tendency to act as a short term flight to a safer asset when the riskier asset gets sold off hard. So even if we are entering a stagflation period, and both stocks and bonds struggle, there will be times when the stock market sells off hard and the bond market will get a little bump up as the least worst short term option.