I don't understand how mutations work, but think you've got it right: "high vaccination is needed, etc..." That's what herd immunity would be, I believe.
This comparison includes AstraZeneca but does not include the Delta variant.
https://www.yalemedicine.org/news/covid-19-vaccine-comparisonOxford-AstraZeneca
This vaccine, which is currently being distributed in the United Kingdom and other countries, is distinguished from some of its competitors by its lower cost—it’s cheaper to make per dose, and it can be stored, transported, and handled in normal refrigeration for at least six months. Some countries temporarily suspended use of this vaccine in March after a small number of recipients developed blood clots. In April, a European Medicines Agency (EMA) safety committee concluded "unusual blood clots with low blood platelets should be listed as very rare side effects" that could occur within two weeks of receiving the vaccine. While the U.K. called for further investigation, EMA regulators stressed that the benefits of the vaccine still outweigh the risks.
Status: Not available in the U.S., authorized for use in the European Union (under the name Vaxzevria).
Recommended for: Adults 18 and older
Dosage: Two doses, four to 12 weeks apart
Common side effects: Tenderness, pain, warmth, redness, itching, swelling or bruising at the injection site, all of which generally resolve within a day or two.
How it works: Similar to the Johnson & Johnson's vaccine, this is a carrier vaccine, made from a modified version of a harmless adenovirus. The final product contains the spike protein found in SARS-CoV-2. When that protein reaches the body’s cells, the immune system mounts a defense, creating antibodies and memory cells to protect against an actual SARS-Cov2 infection.
How well it works: AstraZeneca updated its data analysis of its phase 3 trials in March, showing its vaccine to be 76% effective at reducing the risk of symptomatic disease 15 days or more after receiving the two doses, and 100% against severe disease. The company also said the vaccine was 85% effective in preventing COVID-19 in people over 65. The company’s update came a few days after the National Institute for Allergy and Infectious Diseases (NIAID) expressed concern over new data AstraZeneca had submitted in advance of requesting an EUA from the FDA. The NIAID said that data may have included outdated information, which would make its efficacy data incomplete.
How well it works on virus mutations: So far it seems to work better against Alpha variant than the Beta variant. A paper in early February (not yet peer-reviewed) cited 74.6% efficacy against the Alpha variant. However, the vaccine did not protect as well against mild and moderate cases in people infected with the Beta variant. Therefore, South Africa halted its rollout while scientists continue to study whether the vaccine can prevent severe illness and death in people infected with this variant.