With a PoD so late, it might be hard to butterfly away the formation of the HRE, or at the very least, something so close the difference would be minimal.
Ottonians dominated Germany from Saxony and with a strong military power, hence why they were made kings in Germany eventually : having "cleaned their orbit", so to speak and affirmed their power against Late Carolingians of WFrance, Slavic raiders, Italy was a very obvious step for both Henry (which died before going further) and Otto I (in fact, it was a obvious step for anyone managing to take the lead in Germany, as Arnulf's). There are as well institutional reasons : having gathered different territories (Lotharingia, Eastern Francia, etc.) and willing to have an European influence, the imperial legitimacy was certainly the best symbolic asset to get, especially giving Ottonian social-institutional rise was made trough episcopal support.
Not benefiting from this legitimacy would have make Ottonian build-up reaching some limits and obstacles pretty soon : for instance, Bruno recieving the ducal title in Lotharingia was possible because he could bound secular princes to himself much more easily being emperor-king, would it be only giving a derivative for German potentes in Italy, and prevent a clerical backlash if it happened that, able to answer the call of the pope, he decided just not to.
Otto I, had this point, had little choice but to intervene in Italy.
You'd need, to change this, a strong post-Carolingian Italy, which is easier said than done. It's true that Hugues of Arles managed to deal with the worst of Italian feudal anarchy that prevailed in the kingdom, but let's remember that he took his own legitimacy to rule from a pontifical support just as Otto I did. You'd need then more than that.
Eventually, I think having Lothar of Arles surviving would be a good thing on this regard. But would it really prevent the dynastic and aristocratic struggle between Bosonids, Welfs and Invreans to turn Italy into a dynastic hot seat? I think having a situation comparable to IOTL, with a stronger Italy, might be doable.
Meaning that, like Berengar was technically a subservient king under Otto, we could see Bosonids ending up as a subservient dynasty in Italy, especially if an Ottonian support would help them remaining long enough in place, but I doubt they would give this support systematically or unconditionally. But having a stable dynasty and Italian kingship that doesn't gives the excuse of being mostly usurped and badly managed might prevent Bosonids to loose their kingship.
I think that such sub-kingdom of Italy would appear at best like a mega-Papal states geopolitical equivalent (complete with playing Byzantines against Imperials, Hughes having attempted such alliance IOTL) on which Ottonians would have to regularly intervene against, but not entirely able to utterly dominate, and possibly first trying to tie themselves with local aristocracy.
In order to prevent Ottonians getting too much of a dominance on Italy, you might want to limit their success against Slavs and Hungarians, without getting rid of it.
As for its consequences...
It would still mean a strong form of imperium for Ottonians, just not associated with Italian kingship and a direct relationship to Rome. I wouldn't see Ottonians being less powerful ITTL at least up to the XIth century, and they might just as well pull the same thing than Robertians/Capetians IOTL, meaning forging a stable dynasty, with enough luck. But their main source of legitimacy might come from more "national" grounds, and possibly leading to more regional-centered renaissance instead of a big Ottonian Renaissance.
If we go with the aformentioned challenges on their eastern borders, Ottonians might be focused more on Central Europe for a time, playing eastern principalties and peoples and enforcing their overall influences there; and without benefiting from the same kind of sacred influence they got on Latin clergy overall, you might have them having an harder time supporting aristocratic opposition to Late Carolingians in WFrance as IOTL, maybe up to not supporting Robertian claims as much as they did.
Politically, a less powerful Papacy, more tied to Italian potentes might prevent the pontifical universalism to really blossom, at least in the immediate future of the PoDs. Meaning that churches would be relatively more tied to royal power (a bit like they did before Carolingians, even if less so IMO, because the pontifical figure would be still pretty important). But this royal power would be limited to the aristocratic influence : in France it means before the Clunisiac reform that local families more or less managed monasteries and bishoprics. ITTL, I'd still see a Clunisiac reform equivalent happening, but differently and maybe not as quick (although potentes themselves were spiritually tired of the situation).
Ottonians might have more trouble using bishops as trusted administrators, and maybe having to deal with a similar (even if less chaotic) situation than existed in France on this regard.
The Italian kingdom acting as a semi-subservient/semi-independent entity would probably, as I said above, act like a mega-Papal States both easier and harder to really deal with on the long run, especially if we see the continuation and the reinforcement of Italian-Byzantine ties ITTL.
As for Burgundy...As Aquitaine and Italy the place was a mess of various loyalties, hieroglyphic duties and geopolitical disunity. I could see Italian claims on Burgundy being...diversely respected : probably southern Provence would live its own under technical suzerainty, while the northern part would be too close from France or Germany to really last IMO.
Again, it's from two different PoDs and not that hugely likely, but it's plausible and could work with a late change.
