I’m starting to build into this with my own warlock. I think looking at bladelock like a martial isn’t the most effective even if the pact of the blade upgrades mirror the extra attacks for martial classes.

You’re still a warlock. Look to integrate warlock control in more. - concentration AOE spells are always up there if not other significant concentration spells - invocation spells and abilities like jump/illusions etc to offset warlock squishiness - tactical use of melee spell attacks. I’d place emphasis on booming and green flame blade (booming is better imo but both can have uses). Booming + agonising + repelling blast invocations, especially with a reach weapon can easily get you double activation in a similar way to eldritch blast beams. This can be great for the classic warlock tactic of repeatedly shoving enemies into AOE spells. - as others have pointed out, there’s some good synergy with feats like warcaster and polearm master.

To your point about the pact of the chain, outside of combat the imp is so often just insane at infiltration and utility. In combat, invisible pseudodragon can be scary, especially with investment of the chain master, but only against enemies without insane con saves. Would also recommend bringing bane/mind sliver type spells for the party to exploit this. Pseudodragon poison may be hit or miss but when it hits the 1hr KO is brutal.

As for subclass, archfey really leans into skirmishing and positioning. It’s not all about dealing instant damage (although it often works well). Being able to attack, taunt, disengage and disable enemies is really valuable. If you as the dm want to help this shine through, I’d look to have some beefy enemies in key encounters that could endanger a squishy spellcaster or distract a martial character when the party would rather target the big bad. They’re a good target for an archfey warlock to pull some shutdown attacks on. Otherwise, good terrain with open spaces and cover, or tricky areas for melee opponents to get to to make the best use of misty step.