I ways always told you cannot safely plug an extension cable into an extension cable?
Heres what happens,
People chain together extension leads without paying attention to what they are doing. Extension leads end up getting melted and occasionally causing fires. This is especially a problem in the USA due to their lower voltage, and the fact that they have extension leads that are rated lower than the breakers protecting them, but it can happen over here too, especially when reels get involved.
That doesn't mean chaining extension leads is intrinsically unsafe, it means that as with many things in life you need to pay attention to what you are doing. Protect your cables from damage, pay attention to the total load, unwind reels fully before drawing high currents through them or better yet avoid reels altogether (ever looked at stage/event power/lighting setups? extension leads of various types everywhere but no reels in sight), don't buy extension leads from dodgy sellers.
But that is hard to digest down into a soundbite for the hard of thinking, so people get told not to chain extension leads.
Getting back to your situation in an ideal world one would run permanent power to the workshop, but that is not always practical. In the absence of a permanent set-up i'd much rather see extension leads of appropriate length, routed in a way that kept them away from damage chained together than what it sounds like you have at the moment which is cables that are routed unsafely because they are not long enough to do their job.
As to the lights i'd probablly use something like
https://www.amazon.co.uk/Ashley-J804-Maintenance-Terminal-Junction/dp/B00BATALN6 to join the flexes from the lights to each other and to an incoming flex that could be plugged in.
Don't let perfect be the enemy of better.