This reprex shows a little more of what's going on.
library(broom)
library(mediation)
#> Loading required package: MASS
#> Loading required package: Matrix
#> Loading required package: mvtnorm
#> Loading required package: sandwich
#> mediation: Causal Mediation Analysis
#> Version: 4.5.0
model_med <- lm(vs ~ wt, data = mtcars)
model_out <- lm(am ~ wt*vs, data = mtcars)
mediation <- mediate(model_med, model_out, sims = 1000, treat = "wt", mediator = "vs", treat.value = 2.5, control.value = 3.5)
tidy(mediation)
#> Error: No tidy method for objects of class mediate
class(mediation)
#> [1] "mediate"
Created on 2020-04-09 by the reprex package (v0.3.0)
The error message indeed correctly identified mediation as an object of class mediate and class(mediate) confirms it.
The next step is to look at help(tidy), trace back to the index and see the raft of tidy.X method, where X deals with different types of objects, such as tidy.lm, tidy.glm, etc. Without a thorough search I can't confirm that none of these can take an argument of class mediate but it sure looks that way, simply from the class names.
argument_glossary() %>% print(n = Inf)
doesn't seem to offer anything likely.