one of the colorbars is going out of the figure window

The issue you are running into is due to this line of code:

linkprop([ax(1), ax(2)], {'XLim', 'YLim','Position', 'View'});

That line of code is setting the Position property on the axes, which switches the PositionConstraint from 'outerposition' to 'innerposition'.

f = figure;
t = tiledlayout(1,1);
ax(1) = axes(t);
p = pcolor(ax(1), peaks);
set(p, 'EdgeColor', 'none', 'FaceAlpha', 1);
set(ax(1), 'Colormap', bone);
cb(1) = colorbar(ax(1));
cb(1).Layout.Tile = 'east';

ax(2) = axes(t);
p2 = pcolor(ax(2), peaks);
set(p2, 'EdgeColor', 'none', 'FaceAlpha', 0.5);
set(ax(2), 'Colormap', copper);
cb(2) = colorbar(ax(2));
cb(2).Layout.Tile = 'north';

ax(2).Visible = 'off';
ax(1).XAxis.FontSize = 14;
ax(1).YAxis.FontSize = 14;
ax(2).XAxis.FontSize = 14;
ax(2).YAxis.FontSize = 14;
ax(1).FontSize = 14;
ax(2).FontSize = 14;

xlabel(ax(1),'x(\mum)');
ylabel(ax(1),'y(\mum)');

Note: When you call linkprop, you have to store the output handle, otherwise the link will be broken immediately. The output from linkprop is a link object that "owns" the link. If you don't store that object, then the link object will be stored in ans, but that will be cleared as soon as the next command runs. Once that link object is cleared, the link will be broken.

link = linkprop([ax(1), ax(2)], {'XLim', 'YLim','View'});