[BUG] dcc.Markdown mishandles escaped dollar inside math expression #4122

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Describe your context

• Dash version: 4.5.0
• Minimal example:

from dash import Dash, dcc

app = Dash(__name__)
app.layout = dcc.Markdown(
    r"""
    control: $\approx 3,150$

    escaped dollar: $\approx \$3,150$

    double backslash: $\approx \\$3,150$

    two-dollar delimiters: $$\approx \$3,150$$
    """,
    mathjax=True,
)

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

In Dash 4.5.0, the escaped-dollar example is parsed/rendered incorrectly. The control case, the double-backslash example, and the $$...$$ example work as expected. The problematic input is r"escaped dollar: $\approx \$3,150$", where the intended escaped dollar inside the math expression is not preserved correctly.

Describe the bug
With dcc.Markdown(mathjax=True), an escaped dollar sign inside an inline math expression causes the expression to be parsed/rendered incorrectly. This appears to be a regression in the Markdown/math parsing pipeline introduced by the Markdown rewrite in PR #3960. The current regression test covers escaped dollar signs in ordinary Markdown text (outside math), but not an escaped dollar inside $...$.

Expected behavior
The escaped dollar should remain a literal dollar sign within the math expression, and the expression should render as intended. For example, r"escaped dollar: $\approx \$3,150$" should render approximately followed by $3,150.

this test works fine on Dash 4.4.1

Screenshots