set_props only updating last output in background callbacks

Describe your context
Mac OS, occurring in Safari & Chrome

dash                 2.18.2
dash-core-components 2.0.0
dash-html-components 2.0.0
dash-table           5.0.0

Describe the bug

When updating two different components via set_props, in a background callback with running, only the last output is updated. No console errors encountered.

Further testing:

• If I remove the background, and running, then both outputs are updated as expected.
• The issue persists if I replace running with cancel.
• If I swap the order of the set_props lines, the other component updates instead.

See reproducible example below:

from dash import Dash, Output, Input, html, set_props, DiskcacheManager
import diskcache
import dash

cache = diskcache.Cache("./cache")
background_callback_manager = DiskcacheManager(cache)

app = Dash()

app.layout = [
    html.Button("start", id="start"),
    html.Div("initial", id="output"),
    html.Div("initial 2", id="output-2"),
]

@app.callback(
    Input("start", "n_clicks"),
    background=True,
    running=[
        (Output("start", "disabled"), True, False)
    ],
    manager=background_callback_manager,
)
def on_click(_):
    set_props("output", {"children": "changed"})
    set_props("output-2", {"style": {"background": "red"}})

if __name__ == "__main__":
    app.run(debug=True)

Expected behavior

All outputs should update, not just the last one.

Start with the set_props calls in the provided background callback reproduction and compare behavior with background, running, and cancel enabled or removed. Trace how callback outputs are collected, and consider the issue done when both output and output-2 update reliably in the reproduction.