Shadi is from the Persian šādī (شادی — joy, happiness) — also Arabic shādī (singer). Shadi Hamid — American political scientist. Shadi Davarpanah — Iranian artist. Shadi Paterson — modern American figure.
Shadi does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Shadi reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.