Yes — apple flesh is a healthy treat for parrots, but you must remove every seed first: the seeds release cyanide when digested.
What it means for budgies
There's nothing specific to a budgie that changes the verdict on apple — it's treated the same as for parrots generally. A budgie portion is tiny — a single bite or a little grated amount is plenty.
The full picture on apple
Apple flesh is safe, hydrating, and well liked by almost every species. The danger is the seeds, which contain amygdalin — a compound that releases cyanide during digestion. A parrot that grinds up several seeds can ingest a meaningful dose.
Core the apple and remove every seed before offering.
Wash the skin thoroughly or peel if not organic — apples carry pesticide residue.
Slices, chunks, or hung on a kabob skewer all work; most birds prefer crisp varieties.