Please post a picture of the shifter or the model number.
Model number of Shimano shifters are located here,

The length of the rd's cage isn't what determines the largest cog it will handle, it's the position of the jockey pulley. Those Shimano 9-speed road rear derailleurs, even the GS versions, were rated for a 27T maximum rear cog and would usually work with a 30T. Above that it was unlikely to work.

42/23 = 1.83 is your current lowest gear ratio.
34/23= 1.48 Gear ratio by changing smallest ring and using current cassette.
42/28= 1.50 Gear ratio by using a 28T largest cogged cassette and NOT changing small ring.

Get a cassette with a 28T largest cog.
It'll give you almost the same lowest gear and is the simplest solution.
Your chain might need to be lengthened 1 inch. Maybe 2?

https://www.amazon.com/Shimano-Casse...g-goods&sr=1-2

44 is too low for me.. from my previous bike.

what is GS and BITD?
ST5510
Great idea..
I found this Cassette in my local Decathlon : 9 speed 11-32 (11-13-15-17-19-21-24-28-32) but they say its for MTB (360 grammes)
will it work?
https://www.decathlon.ma/cassettes-v...efined-8298767
Should i replace also the rear derailleur?

BITD = Back in the day.

As in a long long time ago when I was very young. 1960 - 1979 is the usual date range I'm thinking of when I reference things by BITD.

GS when talking about Shimano Derailleur's is a mid cage length rear DR. GS is actally part of the part number of the DR. SS is in the PN's of the DR's that have what's considered a short cage.

Regardless of SS or GS, you really need to know the exact part number of your DR. While many have the same specs, there are some that are notably different in their specs even when they are SS or GS.

One of the places you can find the specs of Shimano DR's is here.... https://si.shimano.com

Might take a while to learn were to look. I also don't like their new format. Takes me longer to find what I'm looking for.

Update:
I found this Cassette in my local Decathlon : 9 speed 11-32 (11-13-15-17-19-21-24-28-32).. but they say its for MTB (360 grammes)
will it fit in my bike? Should i replace also the rear derailleur?
https://www.decathlon.ma/cassettes-v...efined-8298767

The whole point of NOT exceeding 28T was your current RDER should handle a 28T since it is only 1 T greater than the rated max. Shimano tends to be conservative.
I wouldn't expect them to be so conservative that you could exceed by 3T. You "might" get lucky, but I wouldn't count on it.

IF you go to a "mountain" RDER, than the largest cog issue becomes moot.

I was trying to give you the cheapest, simplest solution.
I'm done.

First, thank you..
It's really hard to find parts here, please take a look in that decathlon, the whole store there is 3 cassettes all for MTB's.
Buying online is not possible here for many reasons.. that's why i asked if that one fits.
Other than that one, i need look for a used cassette.
Sorry, I still don't get everything because i'm a newbie at this and my english is not there yet.

The ST-5510 shifter is for either double or triple cranksets. If you decide to add a third ring to your crank.

The third ring that your crankset takes is 74mm bolt circle diameter five arm. This is a common size for smallest chainring in a triple setup. The 30T is probably about the smallest you would want to match with your 42T middle. If all you can find is a 30T ring for 10 speed, it will probably work fine. If you find that it sits too close to the middle, it is easy to add a thin washer between the small ring and the mounting point, (M8 inner diameter should work).

A smallest ring of 30T and a cassette with a large sprocket of about 27T should be all that you need unless you have major mountains to climb.

Your rear & front derailleur should work fine, it was designed for this triple setup.

If you have a Decathlon store you likely have at least one actual bike shop near you. I'd suggest you take the bike to the shop and let them help you decide how to resolve your issue, obtain and install the parts.

Easier too. It looks like you have a long enough cage on your derailleur, but might need a new chain. Neither is a big deal. Maintenance items.