Just to add to what you wrote.
In one sense, we can say that it is true that the Roman liturgy, before it was codified in 1570, was structurally very much the same since the time of Pope Gregory the Great, whose changes in the Liturgy were limited to the addition of a few words in the
Hanc igitur (
nostros in tua pace disponas, atque ab aeterna damnatione nos eripi, et in electorum tuorum iubeas grege numerari), the transfer of the
Pater Noster at the end of the Canon, immediately before the breaking of the bread (prior to his time, the Pater was recited
after the fraction), and the extension of the chanting of the Alleluia after the Gradual at other times besides Eastertide. The only changes that occurred since that time was mostly confined to the addition of other prayers, the famous of these being the addition of the Creed (Rome, conservative as it was, was pretty late in adopting the recitation of the Creed in the Liturgy when compared to other areas - the custom started because the Holy Roman Emperor Henry II insisted that it be included). But otherwise, the structure was left intact.
Most of the differences are in the realm of the gestures and ritual. When Roman liturgy and chant began to be used by the Franks ever since Pepin the Short decreed the adoption of the Papal liturgy in his kingdom, its started to absorb elements from the local liturgies and chants of Gaul (modern France). While the Roman Rite was heretofore characterized by a straight simplicitycompared to the more lavish and elaborate ceremony, say of the East or even some of its neighbors, the Gallican influence helped introduce some of the characteristics we recognize today in the EF such as the prolific use of incense. (Heretofore, incense was only used during the procession to the sanctuary in Rome.)
It is often related that Charlemagne, Pepin’s son, once asked Pope Hadrian I to provide an authentic Roman sacramentary for use throughout the empire, which the latter sent to the court at Aachen around in the year 785-786. The intention was to preserve it as the authentic “standard” of the text attributed to Gregory the Great and to disseminate it throughout all of Charlemagne’s domain through copies, thereby unifying the whole empire under one liturgy - that of Rome. However, the sacramentary the Pope sent soon proved to be ill-suited to the Emperor’s plan: it only contained the liturgy for certain feasts, which would make it ill-adapted to the daily liturgical needs of a parish. (When complaints reached the ear of the Pope, his excuse was saying that he merely picked from the Lateran library what seemed to him to be the ‘best’ sacramentary he had.) Recognizing the obvious unsuitability of the book, the court liturgists decided to correct the text (especially its rather mediocre Latin) and then to augment it with a supplement - derived from the local traditions - so that it could serve for the daily liturgy. The result of this work is the
Hadrianum, aka the Hadrian Sacramentary.
Eventually, this hybrid Roman-Frankish liturgy started making its way into Rome itself, eventually supplanting the ‘original’ Roman Rite altogether. Roman church life was stagnant during the
saeculum obscurum of the first half of the 10th century; there was a liturgical vacuum, which the Gallo-Roman liturgy refilled. This took place both through the direct intervention of the Holy Roman Empire and by the settlement of the Cluniacs in monasteries of Rome or its neighborhood.
Let’s compare for example the Mass as described in
Ordo Romanus I (which describes the Roman liturgy of
circa the early 8th century, and may even in substance reflect the Mass as it was earlier, in the time of Gregory the Great) or
Ordo Romanus IV (aka the Ordo of St. Amand,
circa late 8th century)
Ordo Romanus XVII (of around the same date) with the EF Mass. The ritual is different in many places, but the structure is more or less exactly similar. So yeah, there’s a line of continuity.