I agree the mobilization has to be taken seriously, but I think the only (and best) use of these mobilized troops warm bodies will be throwing them into Crimea and maybe Donetsk, Kherson and Zaporizhia (assuming Donetsk isn't compromised by the time they make it to the front). I think Luhansk is a lost cause at this point as Ukraine will be putting more and more rail in that oblast under artillery range, unless they are willing to march them into Luhansk from the east/south. The problem is that they'll be spotted long before they get near enough to do something.
Regardless of how the mobilized troops act in combat, Russia has some serious issues that will cripple their ability to even get them into combat, or limit where they will see combat:
Crimea: Crimea is the crown jewel, and everything Russia does has to be weighed in terms of whether it safeguards Crimea. I would argue that the mobilization is in part because Putin is afraid Ukraine could get into Crimea. Russia occupying Donetsk, Luhansk, Kherson and Zaporizhia is about protecting Crimea with a land bridge. Opening a front in the north, in theory could pull Ukrainian troops away, but opening such a front reduces the ability to resupply/reinforce Crimea.
Artillery: Back in February when the Russians began moving into the northern Ukraine, the Ukrainians didn't have hyper-accurate NATO artillery (from M777s to HIMARS and everything in between) to counter the Russians, and they didn't have the experienced and well-trained troops manning that artillery that they do now. Every week, the Ukrainians are getting more new artillery and ammo, and they have more and more soldiers who are finishing their training on that artillery. The Ukrainians now have the artillery capacity and capability to disrupt Russian logistics and troop movements at long distances. Think about what Ukraine was able to do in terms of defending Kyiv with what they had in February and March, and that pales in comparison to what they have now. Because Ukraine has great interior lines and very mobile artillery, they can move up artillery fast to deal with any breakout problems.
Logistics: Russians have lost thousands of trucks/personnel carriers that they can't replace (due to sanctions), which really limits their movement of troops in terms of getting them the last 30-40 kms. Ukraine is in the process of putting all of Russia's logistic rail hubs in the northeast under artillery coverage. That means that for an attack in the northeast, Russia would have to bring in heavy equipment/masses of troops/supplies from the more southerly logistics hubs, and those hubs are already strained (due to having to take in logistics traffic that would normally have flowed from the northern hubs). And they've got to move it from those southern/eastern hubs with trucks and personnel carriers that they are running low on. An attack from the north (Belarus) would rely on masses of trucks/personnel carriers they don't have or can't easily spare from the south.
Russian Air Force/Missiles: They are acting like they are on a quota, and just popping off a few dozen missiles a day at civilian targets - this kind of makes me think Putin is in charge of targets, because it's a waste of irreplaceable missiles that should be aiding his military and hitting Ukrainian military targets. Their Air Force seems to be gunshy as well, versus early on in the war. Ukraine keeps chipping away at their air defenses like nobody's business.
Reserves: If Russia attacked from say Belarus, Ukraine has hundreds of thousands of soldiers in their territorial defenses in the rear areas that have been training for months and are better-trained and equipped than the mobilized Russians, that could be moved up quickly because of great interior lines of movement (not to mention the Ukrainian Air Force would come into play). Ukraine could call Putin's bluff and stick with using their regular troops against Kherson/Donetsk/Crimea and leave those mobilized Russian troops to Ukraine's better-trained territorial defenses and Air Force. Putin is then dealing with the fact that he has scarce logistics resources and warm bodies tied up in the north that he would need in south. The mobilized Russians became a liability/drain on defending Crimea, because they've sucked away vehicles that are needed to help with Crimea.
Officers/NCOs: Russia has around 1,200 officers that have been confirmed killed. This includes dozens of battalions and hundreds of companies/batteries losing their commanding officers, and we already know they have battalions and companies that are not only understaffed, but are being led by officers that are a pay grade or two down from what the position normally requires, so the regular Russian army already has a problem with officers/NCOs. And 1,200 dead officers probably means thousands of dead NCOs. If they strip the regular army of experienced officers/NCOs to lead the mobilized Russians, they've fucked over the regular army. If they leave those mobilized troops to being led by mobilized officers and NCOs, they've fucked those mobilized troops.
Heavier Units (Armor): Russia clearly doesn't have the modern armored vehicles (tanks or IFVs/APCs) to supply any large formations that are being wished into existence, otherwise they wouldn't be pulling out old T-62 and T-72s. That means masses of infantry. They would need months to get mobilized troops up to speed on fighting with those vehicles anyways.
Putin is a gambler though, which is really bad for somebody in his situation.
Sorry for the manifesto, waiting on the game.
TLDR: Yes, they have to take it seriously, but Russia is very confined on where they can use these troops.