The GPS jamming conducted by the Russians is not directional, they did not blackout this aircraft specifically, they did this to the entire region. You can easily see that they've already lost GPS tracking when they were still underway to Grozny near Makhachkala, well before they got shot at:
Any aircraft that was flying in that area had their GPS tampered with, not just flight J28243.
And as to why they did that is of course to mess with the GPS tracking of the Ukrainian drones which were active in the region on that day. Anybody with two braincells to rub together would have closed the airspace in the region, but we're talking about Russia.
I do not want to exclude the possibility that they might have hoped to have the aircraft crash into the sea, maybe hiding the traces of what had really happened, especially with how suspiciously quick they were in claiming that the aircraft had suffered a birdstrike and had to divert from Grozny because of fog. They must have quickly realized what had happened and been in utter panic, because nobody would buy those excuses. METAR reports by the Grozny airport are public and for the time in question they show just a bit of mist, but still with 3.5km visibility and lowhanging cloudcover, but well within the minimums needed. And the damage profile of missile shrapnel is drastically different to birdstrikes, if any impartial investigation got their hands on the debris that excuse would also have been refuted quickly. Air crash investigation is so advanced, they had basically no chance of their story ever holding up to scrutiny. But Russian military culture has been so built around deflection, counteraccusation, lies and corruption that I am not surprised that their initial reaction was as seen. It's basically second nature by now.
As for diverting them across the sea, there is actually two good reasons for that. The first is of course the ongoing threat situation with an active air defense. It is way too dangerous for any aircraft to be there. Even if you don't shoot at the aircraft specifically there is always the chance that a missile erroneously aquires it as a target, as the Americans had also had to learn a few days prior when the USS Gettysburg shot down one of their own F/A-18 Super Hornet fighter jets with a missile it had aimed at Huthi drones. The second reason is that the weather in the region was not great for an emergency landing. With a fully intact and functioning aircraft it was well within the minimums needed, but with a heavily damaged aircraft with no flaps/slats and severely impacted handling it would have added an unreasonably large complication. As long as there was no deteriorating situation and they had enough fuel, diverting somewhere with better weather under those circumstances could actually be seen as reasonable.
However... if you ask me, neither of those good reasons played a role, they just panic-reacted and wanted it out of their hands and area of responsibility, and let someone else deal with it.