I'm experiencing a similar issue but with an inheritance project:
I cannot use the specified parameter name "SVN_BRANCH" to trigger the project from another project. It falls back to the default value.
The "Build with Parameters" pages shows the correct name for the parameter but the "Parameter" page displays "Tag" and "Repository URL".

It seems that parameters of type ListSubversionTagsParameterValue are not recorded as a groovy variable in a workflow run automatically. But it is possible to get access to the two embedded values "tag" and "tagsDir" using the following code inside a workflow run (assuming the parameter is named "SVNTAG"):

def SVNTAG = currentBuild.rawBuild.getAction(hudson.model.ParametersAction).getParameter("SVNTAG")
println("Tag: ${SVNTAG.tag}, URL: ${SVNTAG.tagsDir}")

Is it actual way to get SVNTAG.tagsDir now?

def SVNTAG = currentBuild.rawBuild.getAction(hudson.model.ParametersAction).getParameter("SVNTAG")
println "${SVNTAG.tagsDir}"

returns null.
Among the environment variables, there is only one containing the tag value (that early was SVNTAG.tag)

Unfortunately, SVN List Tags parameter is still not working with the "params" global variable.

But, the code mentioned above should still work (assuming you named your parameter SVNTAG). I'm currently using a custom step which more or less does the same as the code above but is more flexible as you can simply pass the name of the parameter to the call to get the parameter:

def call(name) {
  def listTagsParameters = currentBuild.rawBuild.getAction(hudson.model.ParametersAction).parameters.findAll { it instanceof hudson.scm.listtagsparameter.ListSubversionTagsParameterValue }
  def p = listTagsParameters.find { it.name == name }
  // ListSubversionTagsParameterValue class is on blacklist and cannot be used in a sandboxed environment, return a map with strings resembling the relevant properties of the object
  return [name: p.name, tag: p.tag, tagsDir: p.tagsDir]
}

Add this to your custom shared library in "vars/" directory and name it e.g. svnListTagsParameter.groovy. You are then able to simply call something like this to get the parameter:

def p = svnListTagsParameter("PARAMETER_NAME")
println("Name: ${p.name}, Tag: ${p.tag}, Tags dir: ${p.tagsDir}")

Oh man thank you so match!