Nothing converges with the latest version of the dependencies

[Sbozzolo]

Steps to reproduce:

1. Clone ClimaTimeSteppers
2. Change line 116 in docs/src/plotting_utils.jl to true
3. Run julia --project=docs docs/src/dev/report_gen.jl

Observe lack of convergence:

[ Info: Running ark_analytic_nonlin with SSP22Heuns...
[ Info: RMS_error(dt = 0.5) = 2.8790922278623774
[ Info: RMS_error(dt = 0.15873015873015872) = 2.882350814341389
[ Info: RMS_error(dt = 0.05) = 2.88247271669613
[ Info: RMS_error(dt = 0.015822784810126583) = 2.8824266020839087
[ Info: RMS_error(dt = 0.005) = 2.8824038021058023
[ Info: Order = -0.0002017963909637232 ± 0.0006704691254099652
┌ Warning: Predicted order outside error bars for SSP22Heuns (ark_analytic_nonlin)
└ @ Main /tmp/ClimaTimeSteppers.jl/docs/src/plotting_utils.jl:227
[ Info: Running ark_analytic_nonlin with SSP33ShuOsher...
[ Info: RMS_error(dt = 0.5) = 2.8847372455991263
[ Info: RMS_error(dt = 0.15873015873015872) = 2.882848353308922
[ Info: RMS_error(dt = 0.05) = 2.8825199640011627
[ Info: RMS_error(dt = 0.015822784810126583) = 2.8824312685695137
[ Info: RMS_error(dt = 0.005) = 2.882404266043048
[ Info: Order = 0.00015300637003173238 ± 0.00037551975799387995
┌ Warning: Predicted order outside error bars for SSP33ShuOsher (ark_analytic_nonlin)
└ @ Main /tmp/ClimaTimeSteppers.jl/docs/src/plotting_utils.jl:227
[ Info: Running ark_analytic_nonlin with RK4...
[ Info: RMS_error(dt = 0.5) = 2.884061928472975
[ Info: RMS_error(dt = 0.15873015873015872) = 2.8828283938900365
[ Info: RMS_error(dt = 0.05) = 2.8825193581084463
[ Info: RMS_error(dt = 0.015822784810126583) = 2.8824312495505797
[ Info: RMS_error(dt = 0.005) = 2.8824042654447504
[ Info: Order = 0.00011177099725677508 ± 0.0002435936095226765

This used to work, but we haven't caught when it started breaking because of #297 #283 .