Faster tires for a hybrid bike?

I always thought my Travel Contact were excellent, fast on tarmac and enough side knobbles to give a bit of grip when cornering when the going got a bit rough.  They don't like lots of mud though.

A good amount of rubber in the middle to protect against the p thing too.

I bought the cheapest widest tyres I could find and fit and get no punctures on loose gravel and bumpy tracks. The air volume helps stability and power transfer. Maxxis Overdrive 38mm front. Can't find rear tyre brand. 32mm+35mm (2 bikes slightly different tyre width acceptance) . The Wiggles cheapies, buy 4 get free postage.
During summer I'm often on a fixed gear racer using 28s. That's faster but only faster on smooth roads and doesn't carry extra weights.
38/32 a gorgeous combination. You can lean into it and flog it up a hill, across a bumpy track and on smooth it's only a slight wind loss if any.
The square foot print rather than a long skinny foot print is usually less of a rolling resistance.

On tarmac I love 28mm Maxxis Refuse with liners. But during cold nights my luck changed and punctured a few..
I agree with Argos74.. The bloke I bought my last bike from rides a mountain bike with road tyres. Although wide, their smooth tread is fast.
During summer the 28 mm Refuse suits me but I wouldn't like gravel nor dodgy bumpy bike tracks; just smooth road.
32mm road tread rear hammers along nicely with a 38mm front. Absorbs bumps, never bothered with punctures, resistance is aero (not rolling) hence on none race track smooth routes the speeds are often higher and with comfort.

Speed and light offroad capability/tyre width aren't necessarily contradictory. At the moment you're running aggressively offroad tyres, which are fine if you want to keep traction in heavy mud. Put them on tarmac, and everyone suffers.

Go as wide as you can, but ease up on the aggressive centre tread. I've long been a fan of Continental Doublefighters (37mm), which will happily stay the pace on group road rides, and then rock dry singletrack and hardpack trails where the roadies dare not ride. Narrower - and wider - tyres with a similar profile are available depending on how much clearance you have.

I've been using Panaracer Gravel King SK (small knob) 32s for the past few months and like them a lot. They roll well on the road and have so far handled a bit of rough stuff (stony tracks, gravel, rubbish roads) nicely. Haven't tried mud or sand, but I wouldn't bet on them being up to much - horses for courses.

Conti GP 4 Seasons are also excellent and available in 28 and 32. I use them year round on the road-road bike and they've very good puncture protection and grip. Not that great at loose stuff though

I've used 32mm Schwalbe Marathon Plus for many years because I hate getting punctures whilst commuting; however they 'weigh a ton' so I'm thinking of giving Marathon Supremes a go.  Good puncture protection, much lighter and good rolling resistance, but a thin side-wall which is an issue for some people.  I reckon if you want lightweight, fast rolling and good puncture protection, you're going to have to pay but there are always good deals to be had on-line.

32mm is your sweetspot for all terrains IMO but 28mm for the front if you are going to that size, a decently fast tyre are these  https://www.planetx.co.uk/i/q/TYPAJBG/jack-brown-green-folding-tyre

I've used Specialized Pro folders in 32mm but they no longer produce them and I'm on my last of my stock so bought the Jack Brown's, not quite as tough as the Spesh tyres but not bad.

Panaracer also do a 32mm and there's the ubiquitous voyager hyper.

I would agree that tyres of around 28-30mm are ideal for most hybrids, they were my choice when I was commuting in all weathers.  But I can't support your pick of the Conti range, I'm afraid, although it's not the manufacturer that worries me, it's the price.  Having long, long experience of many kinds of rubber, and having made every possible mistake, I have eventually arrived at the point where I accept that you will only get what you pay for.  Too late in life to do me much good I now happily cough up for premium tyres because they are worth every penny.

Take no notice of makers' claims of puncture resistance or long life or of pretty photos of sunsets on the trail.  Concentrate instead on the thread count, the multi-layer construction and the tread you want.  And read the reviews in the magazines, both online and in print.  Try the very interesting bicyclerollingresistance.com for details of their test results.

There are dozens to choose from and I won't bore you with a list of my favourites, but as a rule of thumb you should expect a decent pair to lighten your wallet by at least £70.   If you decide to go tubeless, and that's a whole other discussion, you can add thirty quid to that. 

But hey, it's only money and I can't think of a single component that better deserves your cash.

Best of luck.