mRNA vaccine technology has existed for a few decades, but research and development has only heated up in recent years as the tech has improved.

mRNA vaccine candidates went through early stage Phase I clinical trials for diseases such as influenza in 2015-2018, as well as Zika virus and RSV in 2019. Results from the influenza trial suggest the mRNA vaccine was safe, but as it was only a Phase I trial was not designed to test for the effectiveness for preventing infection, severe disease, or death. None of these mRNA vaccine candidates appear to have progressed past Phase I trials.

The mRNA COVID-19 vaccines are the first mRNA vaccines to make it through Phases I and II, being initially rolled out to the public under Emergency Use Authorization instead of full approval since Phase III trials are still ongoing.

Importantly, viral-vector DNA vaccines like AstraZeneca and Johnson&Johnson share many similarities to mRNA vaccines, in that they teach your body to grow spike proteins in order for you to develop antibodies to those spike proteins. The way they get there is slightly different but the overall goal is the same. Deliver genetic material into some of your cells to make those cells grow spike proteins.

The only previously approved-for-the-public DNA vaccines were for Ebola in 2019 and 2020. Viral-vector DNA vaccine candidates were studied for respiratory pathogens in the past such as SARS and MERS, but conclusively failed clinical trials as they caused Antibody Dependent Enhancement. This is when being vaccinated results in more severe disease than being unvaccinated:

Immunized ferrets developed a more rapid and vigorous neutralizing antibody response than control animals after challenge with SARS-CoV; however, they also exhibited strong inflammatory responses in liver tissue. Inflammation in control animals exposed to SARS-CoV was relatively mild.

^{https://journals.asm.org/doi/full/10.1128/JVI.78.22.12672-12676.2004}

VRP-N vaccines not only failed to protect from homologous or heterologous challenge, but resulted in enhanced immunopathology with eosinophilic infiltrates within the lungs of SARS-CoV–challenged mice.

^{https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0030525}

Prior Immunization with Severe Acute Respiratory Syndrome (SARS)-Associated Coronavirus (SARS-CoV) Nucleocapsid Protein Causes Severe Pneumonia in Mice Infected with SARS-CoV

^{https://www.jimmunol.org/content/181/9/6337.short}

The issue with ADE is that it's not specific to DNA or mRNA vaccines, it's mostly a factor with coronaviruses in general. Other vaccine types including the tried-and-true inactivated virus vaccine have struggled with the same problem:

Double-Inactivated Severe Acute Respiratory Syndrome Coronavirus Vaccine Provides Incomplete Protection in Mice and Induces Increased Eosinophilic Proinflammatory Pulmonary Response upon Challenge

^{https://journals.asm.org/doi/full/10.1128/JVI.06048-11}

Immunization with inactivated Middle East Respiratory Syndrome coronavirus vaccine leads to lung immunopathology on challenge with live virus

^{https://www.tandfonline.com/doi/full/10.1080/21645515.2016.1177688}

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TL;DR: mRNA vaccines are new, viral vector DNA vaccines are new, but the biggest thing people are concerned about is that trying to create a vaccine for any type of coronavirus is still very new and has faced significant safety challenges.

Studies have already shown that the mutations that produced the current Delta variant shifted the balance towards ADE and that a few mutations to the existing Delta variant would cause ADE.

I kinda went off on a tangent there but hopefully the info is helpful.