As far as I can tell this topic, specifically for human papillomavirus (HPV), hasn't been fully investigated. There is some literature on it (as cited by OP), but it is sparse, making this an open field for someone to investigate. As such there is no certainty about how long a sample can persist in the environment as a huge number of factors come into it.
However, this is a difficult topic to investigate - how do you mimic in the laboratory the conditions under which you would find the virus in a natural shedding? In terms of HPV, no-one seems to have fully investigated just how the virus is deposited in terms of how it is shed in a natural manner from warts. It is assumed in the literature that it is in the form of keratinised squamous epithelial cells with virus inside, and probably naked virus too. These will have different profiles of decay in the various environments because of the natures of the different forms.
In terms of environments for persistence, there are a huge number of factors that might play into it. Here are a few of the known significant ones: heat (max temperature and min temperature as well as freeze/thaw cycles), light (particularly UV from sun), humidity (overall in environment and local to the place were the virions are), salinity (beach?), chemical (e.g. chlorine at a pool), how the virus is deposited, and last but not least, what the virus is in (a skin cell? mucus? naked virion?)
HPV is a non-enveloped virion containing double-stranded DNA. The virion is composed of 72 capsomers each consisting of 5 copies of the structural protein L1 and forms a strucutre with icosahedral symmetry. The capsid is capable of self-assembly under the right conditions, which means that it is likely quite stable (relative to some other viruses), as it can potentially re-form if damaged by heat or something similar.
The virus enters the cell through abrasions or micro-traumas of the skin surface, where it invades the squamous epithelium and only grows in those keratinized cells. It can also invade and grow in epithelial tissues of some mucosa such as the nasal passages, throat and vagina. Some of these tissues are shed containing virus through abrasion and natural shedding of the epithelial surfaces.
Now that we have a bit of the biology out of the way:
How do we test for persistence of a virus in the laboratory? Actually it is quite simple, generally you grow and purify the virus (or a surrogate similar virus) and then place some as droplets on the surface you wish to test. You then subject it to the conditions that you want to mimic and see how long you can detect it for.
The methods of detection vary depending on the virus and study. Some will use molecular detection methods like the ability to PCR amplify genetic material from the virus as a surrogate for genetic damage making the virus incapable of replication. The other most commonly used is to try to propagate the virus from swabs taken from the surface it was applied to. This doesn't work for all viruses, as some are not culturable, or are very difficult to culture (e.g. for SARS-CoV-2, only about 30% of positive samples can be cultured, but for measles virus very close to 100% can be cultured). If the virus is not culturable, it may be that it can get into the cell and either replicate but not escape the cell, or that replication is incomplete, so genes are expressed, but no virions formed. If either of those two options are go then the presence/viability of the virus on the surface can be determined by looking for activity of one or more viral genes.
I can't give you landmarks for HPV, and the exact sequence of events is unknown for any of the viruses I know anything about, but in general viruses tend to be non-viable before you can no-longer detect genetic material. Exactly how long each of these takes depends highly on the virus. For instance, take two quite topical viruses - SARS-CoV-2 and influenza, both enveloped (less stable) RNA viruses with similar size and structures and similar routes of transmission. Viable influenza persists for about 2 weeks on stainless steel, but only 1 week on cotton, but you can detect the RNA for up to 17 weeks, while CoV-2 only persisted for 1 week on steel, but RNA could be detected for the full duration of the study (though I can tell you personally from my CoV-2 as yet unpublished results >14 days on some surfaces under some conditions at room temp).