Is performing ghusl and saying the Shahada after having intrusive doubts about faith, and then feeling joy in the certainty that follows, considered a sin if the Prophet, peace and blessings be upon him, commanded us to ignore intrusive doubts?

Indulging in whisperings (waswas) is a grave evil. The cure for it is complete avoidance and not paying any attention to them, because they do not end; rather, some generate others.

What happened to you—the whisperings after ghusl (ritual bathing)—is a continuation of the waswasa. You must completely close this door and cast away all such whisperings.

Know that you do not sin by performing ghusl, and your joy is not joy over a sin; rather, it is your belief in repentance and faith.

What is best for you is complete avoidance of whisperings. Whenever a whispering concerning faith presents itself to you, seek refuge with Allah, say "I believe in Allah," and then stop and do not pay attention to it.

The preponderant opinion is that ghusl is not obligatory for someone who embraces Islam unless they committed something during their disbelief that would necessitate ghusl.