Yes, totally normal lah! My girl went through the exact same thing around that age, and her infant care teachers said it's actually a developmental milestone - means she's understanding object permanence and has formed secure attachments, which is a good thing. It usually peaks between 6 to 9 months and then gradually gets better, especially if you keep the routine consistent and don't make a big fuss when you leave (I know easier said than done). The crankiness at school should settle down as she gets more used to the environment again, but it can take a few weeks. Just keep reassuring her when you pick her up and try not to sneak away - a calm goodbye actually helps more than you'd think.
Oh my, my little one went through exactly the same phase around 7 months old! It’s totally normal separation and stranger anxiety, even if they’ve been in childcare since 4 months. Babies’ brains develop fast at this age, they suddenly understand “mom can leave”, which triggers the fussiness. It is temporary, though it can feel tough right now. My baby also got upset with new people and hated me stepping away for even a minute. It makes sense she gets fussy at school. Be patient, this developmental stage will fade in a few months. You’re doing great!