“belief ‘in’ a thing such as ... a piece of cloth is not right.”
I bet the people who were healed by Paul handkerchief (Acts19:12) might disagree with you. The woman with the hemorrhage touched the hem of Jesus’ robe and was healed. Peter’s shadow healed (Acts 5:15).
I’m not saying that one should worship a handkerchief, a robe, or a shroud as objects. But items connected to holy people can be venerated.
I'll bet that when Paul discarded the cloth that it no longer had healing powers...And I'll bet that when Jesus' robe was discarded, no one after was ever healed from touching it...
I have no doubt that many people touched Jesus robe while he was wearing it who were never healed of anything...