三十分前後 and 三十分以内: an approximate time and an upper limit
Compare a task taking around thirty minutes with a thirty-minute limit, separating an approximation from a strict maximum.
Around a reference value
前後, read ぜんご, can mean approximately a stated amount. 作業は三十分前後かかります。 says that the task takes around thirty minutes.
The duration may be shorter or longer than thirty minutes. 前後 alone does not fix the exact amount of variation allowed.
A range that does not exceed the reference
以内, read いない, identifies a range not exceeding the reference. 三十分以内に終えてください。 requests completion within thirty minutes.
A thirty-minute upper limit includes thirty minutes. A duration of thirty-two minutes does not satisfy 三十分以内.
A request and a completed event
三十分以内に終わりました。 says that completion occurred within thirty minutes. It does not specify that the duration was exactly thirty minutes.
An estimate using 三十分前後 does not itself define a complete deadline condition. Check a separately stated maximum if an upper limit is needed.
Does 三十分以内に終わりました。 require a duration of exactly thirty minutes?
Show the answer and why
No. It says that completion occurred without exceeding thirty minutes. A shorter duration also fits that range.