I was a secondary Modern Foreign Languages teacher and I have fairly good knowledge of grammar. Pearson invited MFL GCSE examiners to mark KS2 SPaG tests, because it was considered that we had the skills needed. MFL teachers often boast that they have a better knowledge of grammar than English teachers, but even they would have been pushed to achieve full marks.
It is very useful for pupils to arrive in secondary school having a firm grasp of the basic parts of speech and to know, for example, that 'run' can be a verb and a noun. However, some of the terminology used in the KS2 tests isn't even the same as secondary MFL teachers use. Either pupils will have to be retaught or secondary teachers will have to change the terminology they've been using for decades.
I hadn't a clue what a frontal adverbial is, so I looked it up. In my opinion, the DfE is misleading. Some of the examples given are indeed adverbial phrases, which have been place at the beginning of the sentence. In some cases they sound very unnatural and I wonder why on earth anybody would want to use that word order. More importantly, some of the examples given aren't adverbial phrases, but subordinate clauses.
I would love to know the background of whoever devised these tests, because it doesn't appear to have been on Planet Earth. Ten and eleven year olds are being forced to learn terminology which probably won't improve their English. When they arrive at secondary school, the teachers of the subject for which grammar is most useful, will just sigh and teach them the terminology they've always used.