Here's a summary of the recently decided (Feb 13, 2020) N.D and N.T. vs Spain case, which was mentioned in the accepted answer. The Grand Court
addressed whether the removal of the applicants amounted to an expulsion or ‘non-admission’ of entry. The GC interpreted expulsion in the generic sense, consistent with previous findings, to mean any forcible removal irrespective of, inter alia, the lawfulness of an applicant’s stay. Indeed, a collective expulsion is characterised as an absence of a reasonable and objective examination of each applicant’s particular case. In the present case, both requirements were satisfied.
However, the GC also highlighted, in accordance with its settled case law, that an applicant’s own conduct is a relevant factor in assessing the protection afforded under Article 4 Protocol No. 4. Indeed, in situations applying to persons who cross a land border in an unauthorized manner, taking advantage of the group’s large numbers, the GC will consider whether the respondent State provided genuine and effective access to means of legal entry. In this case, the GC was not convinced that the State had failed to provide such access, and concluded that the applicants had in fact placed themselves in jeopardy by participating in storming the border rather than using the existing procedures. In particular, the GC observed that the applicants could have applied for visas or for international protection at a border crossing point. It concluded that the applicants’ expulsions did not violate Article 4 Protocol 4. However, it added that this finding does not alter the broad consensus within the international community regarding the obligation for States to protect their borders in a manner compliant with Convention rights, highlighting in particular the principle of non-refoulement.
Furthermore, the GC found that the applicants placed themselves in an unlawful situation by deliberately attempting to enter Spain as part of a large group rather than using available legal procedures. The lack of available individual procedures to challenge the removal was therefore deemed a consequence of the applicant’s unlawful attempt to gain entry. The GC held there was no violation of Article 13 in conjunction with Article 4 Protocol 4.
In view of this, "storming the border en mass" is indeed unlikely to result in anything but (now clearly legal ECHR-wise) pushback.
There's also more commentary (not sure if entirely correct) that
This decision repeals a previous ECtHR judgement of 2017 which had condemned push-backs and which Spain had asked to be referred to the Grand Chamber.
The "repeal" seems to refer to preliminary ECHR judgement in the same case.
The same Verfassungsblog page says that the UNCHR had concluded (in its testimony to the European court) that the provision for visa applications was basically legal fiction, with only a couple of applications being made over the years in that border area. But nonetheless the ECHR thought it was paramount. (I think this is important in regard to the Greece events as well.) Also that blog says that shooting in the direction of boats or swimmers has been done before, by Spain in this case:
Migrants trying to reach the Spanish enclaves by sea are equally liable to be pushed-backed to Morocco. Actually, one of these cases put the public spotlight on Spain’s interventions at the border: in February 2014, Spanish Guardia Civil prevented a group of people from swimming to the Spanish enclave of Ceuta, even firing rubber bullets, with the result of 15 migrants drowning near El Tarajal beach.
Apparently no legal action was taken on that, but rather Spain passed an even more draconian border law in the aftermath.
N.B. an (informal) terminology that is used to discuss this kind of summary rejection (pushback) is "hot returns" or “hot deportation.” (slightly different from "express deportation" as a summary written order is used in the latter, but not the former).
An article in the Guardian makes it more clear that the latest N.D. & N.T. ECHR decision was indeed an appeal
The grand chamber’s ruling comes three years after the same court unanimously ruled Spain had violated rules that prohibit collective expulsion and had denied the right of effective remedy. The latest ruling followed an appeal by Spain.
The 2020 GC decision was also unanimous. Also surely of relevance:
the governments of France, Italy and Belgium ended up joining Spain’s appeal, indicating that the verdict could have a huge impact on the future of Europe’s migration policies.