Yak-130 is perfectly capable of being light multirole fighter if equipment is fitted to it.
The real problem is that some people think it would be a good fighter... and it likely would merely be band aide solution.
Keep in mind that while being relatively light and cheap compared with an expensive medium or heavy fighter, and also relatively manouverable, it would also be largely blind and short ranged and unable to keep up with other aircraft.
Against strike aircraft with target information coming from ground control or AWACS, it could fly at medium altitude at high subsonic speed with some R-77s and some R-73s... so basically a MiG-29S armament, but without the radar and without the self defence avionics... you could send it out to engage enemy bombers and indeed incoming cruise missiles... but actually targeting those would not be 100% easy or reliable... the point is that most of the targets wont fire back.
You could equip it with light bombs, or against targets with no MANPADS you could use rockets and bombs, but really most of the time you would want to use it for what it was designed for... training pilots.
You could consider it both a trainer jet and a rather well armed and fast Super Tucano if you want, but it is no MiG-21 by any measure.
You could rip out the two engines and replace them with a single RD-33 with 9 ton thrust and get something that is supersonic... and fast accelerating and use the extra power to add weight for a new decent nose mounted radar, and extra fuel, as well as an onboard self defence avionics suite... but I am afraid your cheap little fighter will get bigger and heavier and rather more costly and also less suited to training.
I would say starting with a good engine as a basis and then designing from scratch a simple light fast aircraft would be a better basis.... normally in design things are pretty critical... too big an engine you get an aircraft that is fast and able to manouver, but with short legs... not enough fuel and again a short legged fighter... no radar and no avionics, you have a blind sitting duck in the presence of enemy fighters...
As I mentioned it could be used as a Super Tucano in the light strike role where there is little to no opposition, but the other option could be to use them as manned fighter drones... ie they fly with fighters... perhaps at much higher altitude and operating closer to the enemy with no radar emissions... and launch missiles at approaching enemy aircraft and once they have no more missiles they can withdraw with the larger fighters still fully armed, but they detected the targets and guided the missiles the Yaks launched, ready for an engagement fully armed.
It would require good coordination, but the small light aircraft would be up to it... the real problem is that such small aircraft do not offer optimal launch parameters for missiles.... they can't fly that high or that fast... perhaps carrying 6 R-37Ms at 10km altitude at 800km/h, which might give them 200km range, which would still be useful enough...
It's ideal for patrolling with recce pods saves you using up flying hours or more expensive aircraft. Of course if you want the next step up u have mig-29m2 then onto mig-35 su family etc. Currently Russia is missing the market for this category.
I don't think there really is a lighter fighter category... a Gripen type entry, would just be a slightly smaller slightly lighter and slightly less capable MiG-35... I would say keep two engines and go for the MiG-29SMT or MiG-29M2 for reduced price fighter that would be effective in most situations and has the upgrade potential to be actually rather capable.
In fact having 30-50 MiG-29M2s... buy a new targeting pod like Sapsan... perhaps 10 of them and fit those ten aircraft with a new AESA radar so it can operate as a more expensive but also more capable leader... buying a carrier based AWACS platform would also benefit most small airforces as it provides better command and control with a better view...
And as Gary says if you wanted to deliver a huge payload for cheap an IL-76, An-12, An-22 kitted out with svp systems etc you now h avec a hideous amount of cheap bombs in the air with a 3-5m accuracy. Imagine what a An-22 could do with that system. You could even put it on lighter aircraft such as An-24/26, An-32, An-74 if you really wanted any cargo plane really. Would have been useful in Iraq and Syria
You could even add a Glonass guidance system for the bombs rather cheaply and just fly a strike aircraft with radar operating to find the ground target and work out their ground coordinates and set the guidance systems on the transport planes and shove them out the back door at about the right time... no modifications needed.