I could solve the problem by creating simple arrays using numpy for surface plotting and switching to go.Surface from Mesh3D. Any solutions concerning the latter are still welcomed.

The complete code:

import pandas as pd
import plotly.graph_objects as go
import numpy as np


data = pd.read_excel(r"C:\Users\canoe\OneDrive\Asztali gép\Malin study (biathlon)\course profile plot_male.xlsx", sheet_name='Munka1')

x = data['x'].values
y = data['y'].values
z = data['alt'].values
i = data['incl'].values


X = np.vstack([x, x])
Y = np.vstack([y, y])
Z = np.vstack([[350] * len(x), z -0.1]) 
I = np.vstack([i, i])

fig = go.Figure()

fig.add_trace(go.Scatter3d(
        x=x,
        y=y,
        z=z,
        mode='lines',
        line=dict(
            color=i,
            width=13,
            colorscale='Jet',
            colorbar=dict(
                title=dict(
                    text='Incline [deg]',
                    font=dict(size=14, color='black')
                ),
                thickness=20,
                len=0.6,
                tickfont=dict(size=12, color='black'),
                tickmode='linear',
                tickformat='.2f',
                outlinewidth=1,
                outlinecolor='black'
            )
        )
    ))

for j in range(0, len(x), 20):
    color_value= i[j]

fig.add_trace(go.Surface(
    z=Z,
    x=X,
    y=Y,
    surfacecolor=I,
    colorscale='jet',  
    cmin=min(i), cmax=max(i), 
    showscale=False,
    opacity=0.7
))


fig.add_trace(go.Scatter3d(
    x=x,
    y=y,
    z=[350] * len(x),
    mode='lines',
    line=dict(color='black', width=3),
    name="Profile Curve"
))


for j in range(0, len(x), 20):
    fig.add_trace(go.Scatter3d(
        x=[x[j], x[j]],
        y=[y[j], y[j]],
        z=[350, z[j]],
        mode='lines',
        line=dict(color='dimgray', width=2),
        opacity=0.6,
        showlegend=False
    ))

fig.update_layout(
    title="3D Course Profile Colored by Incline",
    template='plotly_white',
    scene=dict(
        xaxis=dict(title='Meters north from start position', showgrid=True, zeroline=False),
        yaxis=dict(title='Meters east from start position', showgrid=True, zeroline=False),
        zaxis=dict(title='Altitude [m]', showgrid=True, zeroline=False),
        aspectmode='manual',
        aspectratio=dict(x=1.25, y=1, z=0.7)
    ),
    margin=dict(l=0, r=0, b=0, t=50)
)

fig.show()

Resulting in:

Version nr.2 using matplotlib.pyplot:

I post a simpler solution using matplotlib.pyplot but without edge colouring:

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from matplotlib import cm
import matplotlib.ticker as ticker


data = pd.read_excel(r'')

X_1d = data['x'].values
Y_1d = data['y'].values
Z_1d = data['alt'].values
I_1d = data['incl'].values

fig = plt.figure(figsize=(8, 5))
ax = fig.add_subplot(111, projection='3d')


X = np.vstack([X_1d, X_1d])
Y = np.vstack([Y_1d, Y_1d])
Z = np.vstack([Z_1d, Z_1d + (max(Z_1d)-min(Z_1d))])     #[350]*len(X_1d), Z_1d + 50      (and below twice)
I = np.vstack([I_1d, I_1d])  


norm = plt.Normalize(I.min(), I.max())
colors = cm.jet(norm(I))

fig = plt.figure(figsize=(8, 5))
ax = fig.add_subplot(111, projection='3d')

ax.plot(X_1d, Y_1d, Z_1d + (max(Z_1d)-min(Z_1d)), color='black', linewidth=2)

surf = ax.plot_surface(X, Y, Z, facecolors=cm.jet(norm(I)), rstride=1, cstride=1, linewidth=0, antialiased=True, alpha=0.7)

ax.plot_wireframe(X, Y, Z, color='k', linewidth=1, alpha=1.0)

mappable = cm.ScalarMappable(norm=norm, cmap=cm.jet)
mappable.set_array(I)

cbar = fig.colorbar(mappable, ax=ax, shrink=0.5, alpha=0.7, aspect=5, extend='both', extendrect=True, spacing='proportional', format=ticker.FormatStrFormatter('%.1f'))
cbar.set_label('Incline [deg]', rotation=270, labelpad=15)

cbar.ax.axhline(max(I_1d), color='black', linewidth=1.2, linestyle='--')
cbar.ax.axhline(min(I_1d), color='black', linewidth=1.2, linestyle='--')


ax.set_xticks([])
ax.set_yticks([])
ax.set_zticks([])

ax.xaxis.line.set_color((0.0, 0.0, 0.0, 0.0))
ax.yaxis.line.set_color((0.0, 0.0, 0.0, 0.0))
ax.zaxis.line.set_color((0.0, 0.0, 0.0, 0.0))

ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))

plt.tight_layout()
plt.show()

Resulting in: